Question

the product of two numbers is 12.if there sum is added to the sum of their squares is 32,find numbers

Answer 1

Answer:

3,4

Step-by-step explanation:

Let the numbers be a & b

Given,

a*b = 12

a+b + (a^2+b^2) = 32

.............................................

(a^2+b^2) = (a+b)^2 - 2*a*b [identity]

(a+b) + (a+b)^2 - 2*a*b = 32

(a+b) + (a+b)^2 - 2*12 = 32

(a+b) + (a+b)^2 =  56

(a+b)^2 + (a+b) - 56 = 0

(a+b)^2 + 8(a+b) - 7(a+b) - 56 = 0

(a+b)*[(a+b) + 8] - 7*[(a+b) + 8] = 0

[(a+b) +8]*[(a+b)-7] = 0

a+b = 7

ab = 12

b = 12/a

a + 12/a = 7

a^2 + 12 = 7a

a^2 - 7a + 12 = 0

(a-4)*(a-3) = 0

a=4 or 3

So if a = 3, b=4

Hence numbers are 3,4

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