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Find two numbers whose sum is 27 and product is 182.

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CBSE/Class 10/Mathematics/UNIT II: Algebra/Quadratic Equations/NCERT Solutions/Exercise 4.2

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Let X and Y be the two numbers.Given, X+Y=27 ---- (1) XY=182-----(2) From(1) Y=27-X Substituting in (2) (27-X)X = 182 27X-X^2 =182 X^2-27X+182=0 On solving the quadratic equation (X-13)(X-14)=0 X=13 or X=14 Therefore, X=13 implies Y=14 Or X=14 implies Y=13 read more

Let X and Y be the two numbers.Given,

X+Y=27 ---- (1)

XY=182-----(2)

From(1)

Y=27-X

Substituting in (2)

(27-X)X = 182

27X-X^2 =182

X^2-27X+182=0

On solving the quadratic equation

(X-13)(X-14)=0

X=13 or X=14

Therefore,

X=13 implies Y=14

Or

X=14 implies Y=13

read less
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Tutor

Let first number be x then second number be 27-x. According to question or Let us split middle term. Hence required numbers are 13 and 14. read more

Let first number be x then second number be 27-x.

According to question
      
or 
Let us split middle term.
Hence required numbers are 13 and 14.
read less
Comments

Maths Tutor

Let numbers x, y X+y=27.......I xy=182.........Ki x(27- x) =182 27x-x^2- 182=0 X^2-27x+182=0 (X-13)(x-14)=0 X=13,14 Numbers are 13 and 14
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Tutor

13 and 14 182=2×91=2×7×13=14×13 14+13=27
Comments

13 and 14
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Tutor For Mathematics & Science

13,14
Comments

Let the first number be x & the second number be 27 - x. ATQ, x(27 - x) = 182 or 27x - x² - 182 = 0 ;or x² - 27x + 182 = 0; or x² - 14x - 13x + 182 = 0. or x(x - 14) - 13(x - 14) = 0 or (x - 13) (x - 14) = 0 x = 13 or x = 14 Therefore, the numbers 13 & 14.
Comments

a+b= 27 and ab=182 (which is given) a-b = 1 solving a+b and a-b =1 a= 14 and b= 13
Comments

Let numbers be a, and b. a+b =27....(1) ab = 182, now replace a=182/b in equation 1 182/b + b = 27, multiplying b throughout the equation we get b^2 -27b +182 = 0 b=14 or 13, choose any one if b=14 then a=13 or if b=13 then a=14.
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Professional Teacher and having experience from last 4years.

X=13 X=14
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