Question

If `(a-b)^2=40` and `ab=8`, what is `a^2+b^2`?

Answer 1

56

Explanation:

distribute `(a - b )^2" using FOIL (or any method you use) "`

`(a - b )^2 = a^2 - 2ab + b^2 = 40`

( substitute ab = 8 )

hence `a^2 - 2(8) + b^2 = 40 → a^2 - 16 + b^2 = 40`

`rArr a^2 - 16 + b^2 = 40 rArr a^2 + b^2 = 40 + 16 = 56`

Answer 2

`56`

Explanation:

`color(blue)((a-b)^2=40,ab=8,a^2+b^2=?`

Remember the formula `color(orange)((a-b)^2=a^2-2ab+b^2`

So replace `(a-b)^2` by `a^2-2ab+b^2` in the equation

`rarra^2-2ab+b^2=40`

We know that `ab=8`

So,replace `ab` by `8` in the equation

`rarra^2-2(8)+b^2=40`

`rarra^2-16+b^2=40`

Add 16 both sides

We get,

`rarra^2+b^2=40+16`

`color(green)(rArra^2+b^2=56`