Question

If `a + b = 8` and `a^2 + b^2 = 60`, what is `a^2b^2` ?

Answer 1

The answer is `=4`

Explanation:

`(a+b)=8`

and

`a^2+b^2=60`

Therefore,

`(a+b)^2=8^2=64`

But,

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

So,

`64=60+2ab`

`2ab=64-60=4`

`ab=4/2=2`

and

`a^2b^2=(ab)^2=2^2=4`

Answer 2

`a^2b^2=4`

Explanation:

`"given "a+b=8`

`"then "(a+b)^2=8^2=64`

`"now "(a+b)^2=a^2+2ab+b^2`

`rArra^2+2ab+b^2=64`

`"substitute "a^2+b^2=60`

`rArr60+2ab=64`

`rArr2ab=64-60=4`

`rArrab=4/2=2`

`color(blue)"square both sides"`

`rArr(ab)^2=2^2`

`rArra^2b^2=4`