Question

If $\left|a\right|=\left|b\right|=1$ and $|a+b|=\surd 3$, then the value of $(3a–4b).(2a+5b)$ is?

• A. $-21$
• B. $-\frac{21}{2}$
• C. $21$
• D. $\frac{21}{2}$

Answer 1

The correct option is B

$-\frac{21}{2}$

Explanation for the correct option:

Step 1. Find the value of $(3a–4b).(2a+5b)$:

Given, $\left|a\right|=\left|b\right|=1$

and $|a+b|=\surd 3$

$\Rightarrow$ $|a+b{|}^2=3$

$\Rightarrow$ $|a{|}^2+|b{|}^2+2ab=3$

$\Rightarrow$ $1+1+2ab=3$

$\Rightarrow$ $2ab=1$

$\Rightarrow$ $ab=\frac{1}{2}$

Now, $(3a-4b)(2a+5b)=6+7ab-20$

Step 2. Put the value of $ab$:

$=6+7\times \frac{1}{2}-20$

$=\frac{\mathbf{-}\mathbf{21}}{\mathbf{2}}$

Hence, Option ‘B’ is Correct.