UrbanPro
Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Tuition > if x^2+y^2+z^2=xy+yz+zx then find the value of x^3+y^3+...
✕

Search in

if x^2+y^2+z^2=xy+yz+zx then find the value of x^3+y^3+z^3

Asked by Last Modified  

237 Answers

Follow 85
Answer

Please enter your answer

Tutor

We will work with the RHS part here, (x + y+ z)( x² +y² +z² - xy - yz - zx) Expanding the entire bracket, = x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x =x³...
read more
We will work with the RHS part here, (x + y+ z)( x² +y² +z² - xy - yz - zx) Expanding the entire bracket, = x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x =x³ + y³ +z³ - 3xyz This is equal to LHS Hence proved read less
8 Comments
Dislike Bookmark

Tutor

3xyz
2 Comments
Dislike Bookmark

Given- x^2+y^2+z^2=xy+yz+zx ---------(1)multiplying by (x+y+z) on both sides-x^2+y^2+z^2 (x+y+z)=(xy+yz+zx ) (x+y+z)expand the above equations-x^3+y^3+z^3+xy^2+x^2 y+yz^2+y^2 z+xz^2+x^2 z=x^2 y+xyz+zx^2+xy^2+ y^2 z+xyz+xyz+...
read more
Given- x^2+y^2+z^2=xy+yz+zx ---------(1)multiplying by (x+y+z) on both sides-x^2+y^2+z^2 (x+y+z)=(xy+yz+zx ) (x+y+z)expand the above equations-x^3+y^3+z^3+xy^2+x^2 y+yz^2+y^2 z+xz^2+x^2 z=x^2 y+xyz+zx^2+xy^2+ y^2 z+xyz+xyz+ yz^2+ xz^2simplifying -x^3+y^3+z^3=3xyz --Ans read less
Comments
Dislike Bookmark

3xyz
Comments
Dislike Bookmark

As we know (X^3 +Y^3+Z^3)-3XYZ = (X+Y+Z) (X^2 +Y^2 +Z^2-XY-YZ-ZX) given X^2 +Y^2 +Z^2=XY+YZ+ZX I.e X^2 +Y^2 +Z^2-XY-YZ-ZX=0 so (X^3 +Y^3+Z^3)-3XYZ = (X+Y+Z) (0) (X^3 +Y^3+Z^3)-3XYZ=0 (X^3 +Y^3+Z^3)=3XYZ So value of (X^3 +Y^3+Z^3) is (3XYZ)
read more
As we know (X^3 +Y^3+Z^3)-3XYZ = (X+Y+Z) (X^2 +Y^2 +Z^2-XY-YZ-ZX) given X^2 +Y^2 +Z^2=XY+YZ+ZX I.eX^2 +Y^2 +Z^2-XY-YZ-ZX=0 so (X^3 +Y^3+Z^3)-3XYZ = (X+Y+Z) (0) (X^3 +Y^3+Z^3)-3XYZ=0 (X^3 +Y^3+Z^3)=3XYZ So value of(X^3 +Y^3+Z^3) is (3XYZ) read less
Comments
Dislike Bookmark

Tutor

Here, we use formula of x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2-xy-yz-zx) Then x^2+y^2+z^2=xy+yz+zx is given to put the value in an equation.so we get x^3+y^3+z^3=(x+y+z)(xy+yz+zx-xy-yz-zx) x^3+y^3+z^3=(x+y+z)(1) x^3+y^3+z^3=x+y+z............Ans.
Comments
Dislike Bookmark

Home Tutor with 3 years of experience

We will work with the RHS part here,(x + y+ z)( x² +y² +z² - xy - yz - zx)Expanding the entire bracket,= x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x=x³ +...
read more
We will work with the RHS part here,(x + y+ z)( x² +y² +z² - xy - yz - zx)Expanding the entire bracket,= x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x=x³ + y³ +z³ - 3xyzThis is equal to LHSHence proved read less
Comments
Dislike Bookmark

Political Science Honours experienced tutor in Bengali Medium

x3+y3+z3 -3xyz = (x+y+z)(x2+y2+z2 -xy-yz-zx) x3+y3+z3 -3xyz = (x+y+z)(xy+yz+zx -xy-yz-zx) x3+y3+z3 -3xyz = (x+y+z)*0 x3+y3+z3 -3xyz = 0 x3+y3+z3 = 3xyz (Ans.)
Comments
Dislike Bookmark

x^2+y^2+z^2=xy+yz+zx ----eq(1) Identity is x^3+y^3+z^3 - 3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx) x^3+y^3+z^3 -3xyz =(x+y+z)(xy+yz+zx-xy-yz-zx) (acc. to eq1.) Therefore , x^3+y^3+z^3 - 3xyz = 0 So, x^3+y^3+z^3= 3xyz Answer
read more
x^2+y^2+z^2=xy+yz+zx ----eq(1) Identity is x^3+y^3+z^3 - 3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx) x^3+y^3+z^3 -3xyz =(x+y+z)(xy+yz+zx-xy-yz-zx) (acc. to eq1.) Therefore , x^3+y^3+z^3 - 3xyz = 0 So, x^3+y^3+z^3= 3xyz Answer read less
Comments
Dislike Bookmark

Math professional teacher with over 10 years of experience in teaching top institute of India

3xyz
Comments
Dislike Bookmark

View 235 more Answers

Related Questions

Where will you show purchase of computer in cash flow statement?
This is an outflow of cash, and computer is a fixed nature asset so it is shown as an outflow in investing activity
Vijaya
0 0
5
There is any specific details for a teacher to teach IB board specially for language?
Yes, the teacher should be b1 qualified at least.
Oscar Sivale
How do i solve this: A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die ??
Let the probability of obtaining a ‘six’ in a single throw of the die (p) = 1/6 Then, the probability of not obtaining a “six” in a single throw of the die (q) =1-p = 1-1/6 = 5/6 Obtaining third...
Pratik Soni

In durgapur I want to do private tution for classes 1 to 6 all subjects except science, computer and Hindi . Anyone interested ?
Ya
Diya
What is the SI unit of work?
Joules. 1 Joule= 1Newton × 1 meter × cos0
Geetanjali

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Pairs of linear equations in two variables
https://youtu.be/AbnJltTI6CE Pairs of linear equations in two variables

Rumnit

0 0
0
English Comprehension Worksheet
Brain Point Academy Subject- English Practice worksheet Q.1 Read the passage and answer the questions. A mother chicken sat on her nest. She was a big chicken with yellow feathers. She was sitting...
T

Tanvi M.

1 0
0
Organization

Arnab Bhattacharjee

0 0
0
Margin Of Safety In Marginal Costing
Margin of Safety (MOS) is the sale level which exceeds Break Even point i.e. it is the level at which an entity’s output/sales level can fall before a business reaches its breakeven point. It is...

FR Prashanth Reddy

4 0
0
Consignment Meaning & Features
Meaning & Features Of Consignment Meaning: Consignment means the transaction of sending goods by one person (called CONSIGNOR) to another (called CONSIGNEE) who is to sell those goods on behalf of...

FR Prashanth Reddy

Recommended Articles

6 Exam Hall Tips To Follow, For Every Good Student

Appearing for exams could be stressful for students. Even though they might have prepared well, they could suffer from anxiety, tension etc. These are not good for their health and mind. However, following a few exam preparation tips can save them from all these and help them to score good marks. Let’s find out all...

Read full article >

How To Choose The Right School For Children?

Quality education does not only help children to get a successful career and life, but it also hugely contributes to society. The formal education of every child starts from school. Although there are numerous schools, parents find it challenging to choose the right one that would fit their child. It is difficult for them...

Read full article >

The Trend of E-learning and it’s Benefits

E-learning is not just about delivering lessons online. It has a much broader scope that goes beyond manual paper or PowerPoint Presentations. To understand the reach of E-learning and how the whole process works in developing the Educational system, we will discuss a few points here. Let us find out how this new learning...

Read full article >

6 Healthy Habits of School Children

While schools provide formal education to the children, the home is where they start learning about things informally. Parents think that schools will take the initiative to educate their children. Well, this is partially true, as parents also play an essential role in bringing up their child. For the development of particular...

Read full article >

Find Tuition near you
Tuition in Delhi
Tuition in Bangalore
Tuition in Hyderabad
Tuition in Kolkata
Tuition in Mumbai
Tuition in Chennai
Tuition in Pune
Tuition in Lucknow
Tuition in Noida
Tuition in Jaipur
Online Tuition Classes

Looking for Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Tuition Classes?

The best tutors for Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Tuition with the Best Tutors

The best Tutors for Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2025 All Rights Reserved