5(X^2+Y^2+Z^2)=4(XY+YZ+ZX) then find X:Y:Z

Asked by Last Modified  

321 Answers

Follow 28
Answer

Please enter your answer

Vaishnavi

The answer should be -X=Y=Z=0.
Comments
Dislike Bookmark

3 XYZ
3 Comments
Dislike Bookmark

IITIAN DHARMADAS (M.Sc. from IIT GUWAHATI)

Solving the equation you will get (2x-y)^2+(2y-z)^2+(2z-x)^2=0 Since sum of three square number is zero so they are individually equal to 0. So 2x-y=0; 2y-z=0; 2z-x=0 From these three equation we get x=y=z=0
1 Comments
Dislike Bookmark

0:0:0
Comments
Dislike Bookmark

Experienced (10+ Y) & Certified Mathematics Assistant Professor from Uttaranchal University, Dehradun

X=Y=Z
Comments
Dislike Bookmark

A Teacher with 20 years of experience.

In this condition, there is no exact value given for the equation. Hence we cannot solve it without a given state. We cannot find a specific answer for each variable as there are no values given. I also tried the trial and error method, but the answer keeps fluctuating. We might have to create assumptions,...
read more
In this condition, there is noexact value given for the equation. Hence we cannot solve it without a given state. We cannot find a specific answer for each variable as there are no values given. I also tried the trial and error method, but the answer keeps fluctuating. We might have to create assumptions, and then we can solve it. read less
Comments
Dislike Bookmark

Math Tutor ( M.A in mathematics), Experience 14 years

10
Comments
Dislike Bookmark

MATHEMATICS

1:1:1
Comments
Dislike Bookmark

Tutor with an experience in teaching Mathematics since 6 years.

5(x2 + y2 + z2) = 4(xy + yz + zx) or, 5x2 + 5y2 + 5z2 = 4xy + 4yz + 4zx or, 4x2 + 4y2 + 4z2 + x2 + y2 + z2 = 4xy + 4yz + 4zx or, (4x2 – 4xy + y2) + (4y2 – 4yz + z2) + (4z2 – 4zx + x2) = 0 or, (2x - y)2 + (2y - z)2 + (2z - x)2 = 0 We know that, since sum of squares is 0, each square...
read more
5(x2 + y2 + z2) = 4(xy + yz + zx) or, 5x2 + 5y2 + 5z2 = 4xy + 4yz + 4zx or, 4x2 + 4y2 + 4z2 + x2 + y2 + z2 = 4xy + 4yz + 4zx or, (4x2 – 4xy + y2) + (4y2 – 4yz + z2) + (4z2 – 4zx + x2) = 0 or, (2x - y)2 + (2y - z)2 + (2z - x)2 = 0 We know that, since sum of squares is 0, each square must be equal to 0. Therefore, (2x - y)2 = (2y - z)2 = (2z - x)2 = 0 or, (2x - y) = (2y - z) = (2z - x) = 0 Therefore, 2x = y, 2y = z, 2z = x. Thus converting all terms in respect to ‘x’ we get, y = 2x z = x/2 Therefore, x : y : z = x : 2x : x/2 = 1 : 2 : ½ = 2 : 4 : 1 Answer: x : y : z = 2 : 4 : 1 read less
Comments
Dislike Bookmark

Computer Professional Teacher with more than 15 years of experience in Computer Science

X:Y:Z=1:1:1
Comments
Dislike Bookmark

View 319 more Answers

Related Questions

I have now completed B.Tech in Mechanical Engineering. I want to start teaching Mathematics for class 9th upto 12th leve, physics up to 10th level and also capable to teach Engineering math. Please guide me how I can start my career in this field?
Why don't you approach the junior colleges, that's the best place to start your career. Best of luck
Balmikee
Name the Bio-reserves of India.
Nilgiri Biosphere Reserve, Gulf of Mannar Biosphere Reserve,Sundarbans Biosphere Reserve, Nanda Devi Biosphere Reserve, Nokrek Biosphere Reserve, Pachmarhi Biosphere Reserve, Simlipal Biosphere Reserve,...
Jagadeesh
0 0
6
What are Tropical Rain Forests of India?
The Rain forests are known to be found in places receiving more than 230 cms of rainfall and which has a monthly mean temperature of 18C or even higher in the coldest month of the year. They are known...
Md
Dear friends I want to start online teaching. Any one can help me, right now I am fresher in online teaching.
See videos on youtube.
RAKESH MISHRA
2 0
8
How many moles are in 10 gram of Hydrogen Molecules?
5 mol
Rajasree

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

Ask a Question

Related Lessons

Viscometers
The measurement of viscosity is a large and complicated subject. The principles rely on the resistance to flow or the resistance to motion through a fluid. Many of these are covered in British Standards...

Ravi Kumar

5 2
0
Corporate Challenges Of A Finance Professional Today: How to face it?
Dear Corporate Professionals, Past few decades the Global financial services industry and the accounting profession have undergone a sea change with the rapid globalization of economy where Financial...

Venkatesh

1 1
0
Integers Class VII
Natural numbers: 1,2,3,4,5... Whole numbers: 0,1,2,3,4,5... Integers: -3,-2,-1,0,1,2,3... Hence,
A

Aman Garg

0 0
0
Mechanical Properties of Materials
A

Arnab Bhattacharjee

0 0
0
Best Method To Study * Effective Utilization Of Time*
We often sit for long hours to study and at the end of it, we might feel unsatisfied. The time duration of study does not matter, the productivity does. A powerfully curated method that is tried and...

Nitya

1 0
0

Recommended Articles

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 >

Science, Arts Or Commerce - Which One To Go For?

Once over with the tenth board exams, a heavy percentage of students remain confused between the three academic streams they have to choose from - science, arts or commerce. Some are confident enough to take a call on this much in advance. But there is no worry if as a student you take time to make choice between - science,...

Read full article >

Top Benefits of e-Learning

With the current trend of the world going digital, electronic renaissance is a new movement that is welcomed by the new generation as it helps makes the lives of millions of people easier and convenient. Along with this rapidly changing movement and gaining popularity of Internet, e-Learning is a new tool that emerging...

Read full article >

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 >

Find Tuition near you
Tuition in Delhi
Tuition in Bangalore
Tuition in Hyderabad
Tuition in Kolkata
Tuition in Chennai
Tuition in Mumbai
Tuition in Lucknow
Tuition in Pune
Tuition in Noida
Tuition in Gurgaon
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