[tex]ab = 8[/tex] & [tex]a^{2} + b^{2} = 16[/tex] so , [tex]( a+b )^{2} = 32[/tex] .
Step-by-step explanation:
Here we have , ab= 8 & a^2+b^2=16 i.e. [tex]ab = 8[/tex] and [tex]a^{2} + b^{2} = 16[/tex] .
We need to find value of (a+b)^2 i.e. [tex](a+b)^{2}[/tex] :
It's and identity and we know that [tex]( a+b )^{2} = a^{2} +b^{2} +2ab[/tex]
⇒ [tex]( a+b )^{2} = a^{2} +b^{2} +2ab[/tex]
⇒ [tex]( a+b )^{2} = (a^{2} +b^{2}) +2(ab)[/tex]
⇒ [tex]( a+b )^{2} = (16) +2(8)[/tex]
⇒ [tex]( a+b )^{2} = (16) +(16)[/tex]
⇒ [tex]( a+b )^{2} = 32[/tex]
∴ [tex]ab = 8[/tex] & [tex]a^{2} + b^{2} = 16[/tex] so , [tex]( a+b )^{2} = 32[/tex] .
