Question

The sum of two numbers is 8 and the sum of their squares is 34.what is the product of two numbers?

Answer 1

Heya,

Let the two numbers be x and 8-x
x^2+(8-x)^2=34 [here ^ denotes to the power]
x^2+64-16x+x^2=34
2x^2-16x+30=0
x^2-8x+15=0 [on dividing both sides with two]
x^2-5x-3x+15=0
x(x-5)-3(x-5)=0
(x-5)(x-3)=0
x-5=0 or x-3=0
x=5 or x=3

The two numbers are 3 and 5.
The product of the numbers is 15.

#Hope it helps.....

Answer 2

Let the two numbers be x and 8-x

x²+(8-x)²=34
x²+64-16x+x²=34
2x²-16x+64-34=0
2x²-16x+30=0
2(x²-8x+15)=0
x²-5x-3x+15=0
x(x-5)-3(x-5)=0
(x-5)(x-3)=0
x-5=0 or x-3=0
x=5 or x=3

The two numbers are 3 and 5.

Product of two numbers=3×5=15

15 is the answer