Question

If $a-b=4$ and $a+b=6$, find $a^2+b^2$

• A. $26$
• B. $13$
• C. $53$
• D. $40$

Answer 1

The correct option is A $26$

Given,
$(a+b)=6$
$(a-b)=4$
Squaring the above two equation,we get,
$a^2+b^2+2ab=36$ (i)
$a^2+b^2-2ab=16$ (ii)
Adding the two equations, we get
$2(a^2+b^2)=52$
$=>(a^2+b^2)=\frac{52}{2}$
$=>(a^2+b^2)=26$