Question

If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2?

Answer 1

`ab = 8` &
`a^(2) + b^(2) = 16` so ,
`( a+b )^(2) = 32` .

Explanation:

Here we have , ab= 8 & a^2+b^2=16 i.e.
`ab = 8` and
`a^(2) + b^(2) = 16` .

We need to find value of (a+b)^2 i.e.
`(a+b)^(2)` :

It's and identity and we know that
`( a+b )^(2) = a^(2) +b^(2) +2ab`

⇒
`( a+b )^(2) = a^(2) +b^(2) +2ab`

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

⇒
`( a+b )^(2) = (16) +2(8)`

⇒
`( a+b )^(2) = (16) +(16)`

⇒
`( a+b )^(2) = 32`

∴
`ab = 8` &
`a^(2) + b^(2) = 16` so ,
`( a+b )^(2) = 32` .