Question

Given that$\left|a\right|=3,\left|b\right|=4$, and$|a+b|=5$, then $|a-b|$is equal to?

• A. $6$
• B. $5$
• C. $4$
• D. $3$

Answer 1

The correct option is B

$5$

Explanation for correct option:

To find the value of $|a-b|$:

We have,

$\begin{array}{rcl}{\left|a+b\right|}^2+{\left|a-b\right|}^2& =& \left(a+b\right)\left(a+b\right)+\left(a-b\right)\left(a-b\right)\\ & =& a^2+2ab+b^2+a^2-2ab+b^2\\ & =& 2\left({\left|a\right|}^2+{\left|b\right|}^2\right)\end{array}$

Therefore,

$5^2+{\left|a-b\right|}^2=2\left(3^2+4^2\right)$

$\Rightarrow {\left|a-b\right|}^2=50-25=25$

$\Rightarrow \left|a-b\right|=5$

Hence, the correct option is B.