Question

If $(a+b)=7$ and $ab=12$, then .

• A. $(a-b)=\pm 1$
• B. $(a-b)=\pm 2$
• C. $(a-b)=\pm 3$
• D. $(a-b)=\pm 4$

Answer 1

The correct option is A $(a-b)=\pm 1$

Given $(a+b)=7$ and $ab=12$
Using identities we know that,
$(a+b{)}^2-(a-b{)}^2=4ab$
$\Rightarrow$$(a-b{)}^2=(a+b{)}^2-4ab$
$\Rightarrow$$(a-b{)}^2=7^2-4(12)$
$\Rightarrow$$(a-b{)}^2=49-48$
$\Rightarrow$$(a-b{)}^2=1$
$\Rightarrow$$(a-b)=\pm 1$