Question

For integral value of m if the value of $\frac{2}{m}+3m=7$, find the value of $9m^2-\frac{4}{m^2}$ using identities.

• A. 77
• B. 63
• C. 42
• D. 35

Answer 1

The correct option is D 35

It is given that $\frac{2}{m}+3m=7$,
$\Rightarrow$ $\frac{2+3m^2}{m}=7$
$\Rightarrow$ $2+3m^2=7m$
$\Rightarrow$ $3m^2-7m+2=0$
$\Rightarrow$ $3m^2-6m-m+2=0$
$\Rightarrow$ $3m(m-2)-1(m-2)=0$
$\Rightarrow$ $(3m-1)(m-2)=0$
$\Rightarrow$ $(3m-1)=0$ or $(m-2)=0$
$m=\frac{1}{3}$ or $m=2$
For integral value of $m$, we get $m=2$
$3m-\frac{2}{m}=3\times 2-\frac{2}{2}$ $=6-1=5$
Now, $9m^2-\frac{4}{m^2}=(3m{)}^2-(\frac{2}{m}{)}^2$
$=(3m+\frac{2}{m})+(3m-\frac{2}{m})$

$=7\times 5=35$