Question

The sum of two number is 15 and the sum of their squares is 113.Find the number and their product

Answer 1

Since sum of the two numbers is 15,

Let the numbers be x and (15-x)

Then, x²+(15-x)²=113

=x²+(15²-2×15×x+x²)=113

=x²+15²-2×15×x+x²=113

=x²+225-30x+x²-113=0

=2x²-30x+112=0

=x²-15x+56=0

=x²-(8+7)x+56=0

=x²-8x-7x+56=0

=x(x-8)-7(x-8)=0

=(x-8)(x-7)=0

=Either x-8=0 or x-7=0

x=8 or x=7

so, the numbers are 8 and 7

or

7and 8