Question

If $a^2+b^2=13$ and $ab=6$ find $a^2-b^2$.

• A. $\pm 9$
• B. $\pm 5$
• C. $\pm 2$
• D. $\pm 6$

Answer 1

The correct option is B $\pm 5$

$(a+b{)}^2=a^2+b^2+2ab$
$=13+2\left(6\right)$
$=13+12$
$=25$
$=>(a+b)=\pm \sqrt{25}$
$=>(a+b)=\pm 5$
Now,
$(a-b{)}^2=a^2+b^2-2ab$
$=13-2\left(6\right)$
$=13-12$
$=1$
$=>(a-b)=\pm 1$
Now,
$a^2-b^2=(a+b)(a-b)$
$=(\pm 1)(\pm 5)$
$=\pm 5$