Question

Two numbers are such that sum of
their squares is 169 and their sum is
17. Find the product of the numbers.​

Answer 1

Answer:

Let the numbers are x &y

x^2+y^2= 169 ..........(1)

and

x+y= 17......(2)

from equation (2)

y= 17-x ........(3)

put (3) in (1)

x^2+(17-x)^2=169

x^2+ (17)^2+x^2-2*17*x= 169

x^2+289+x^2-34x= 169

2x^2-34x +120=0

dividing both sides by 2

x^2-17x+60=0

x^2-12x-5x+60=0

x(x-12)-5(x-12)=0

(x-5)(x-12)=0

x=5,12

product =5*12=60