Question

If $a+b=7$ and $ab=10$, then find $a-b$.

• A. $\pm 2$
• B. $\pm 7$
• C. $\pm 1$
• D. $\pm 3$

Answer 1

The correct option is D $\pm 3$

Given, $(a+b)=7$, $ab=10$
Squaring both sides
$\Rightarrow (a+b{)}^2=7^2$
$\Rightarrow a^2+b^2+2ab=49$
$\Rightarrow a^2+b^2=49-2\left(10\right)$
$\Rightarrow a^2+b^2=29$
Now,
$(a-b{)}^2=a^2+b^2-2ab$
$=29-2\left(10\right)$
$=29-20$
$=9$
$\therefore a-b=\sqrt{9}$
$=\pm 3$