Question

If $a+b=7andab=6$ , find $a^2-b^2$

• A. $\pm 35$
• B. $\pm 5$
• C. $25$
• D. $-25$

Answer 1

The correct option is A

$\pm 35$

Given
$a+b=7$
Squaring on both sides we get
$(a+b{)}^2=(7{)}^2$
$a^2+2ab+b^2=49$
Given ab = 6
$a^2+b^2+\left(2\right)\left(6\right)=49$
$a^2+b^2=49-12$
$a^2+b^2=37$ ---------------------------------------(1)

$(a-b{)}^2=a^2-2ab+b^2$
$=37-2\left(6\right)$ (∵ $a^2+b^2)=37$ and $ab=6$
= 25 -----------------------------------------(2)
Taking square root on both sides , we have
$(a-b)=\pm 5$

$(a^2-b^2)=(a-b)(a+b)$
$=\left(7\right)(\pm 5$) --------------------------(from (1) and (2))
$=\pm 35$