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 , $( a+b )^{2} = 32$ .

Step-by-step 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 , $( a+b )^{2} = 32$ .