Question

State whether the given statement is true or false.

If $p^{1-2x}\times \sqrt{p}=q^{1-2x}\times \sqrt{q};p\ne q$ then value of $x$ is $\frac{3}{4}$.

• A. True
• B. False

Answer 1

The correct option is A True

As given $p^{1-2x}\times \sqrt{p}=q^{1-2x}\times \sqrt{q};p\ne q$.

when $p$ is not equal to $q$ both sides can be equal only when their power is equal to zero.

$\Rightarrow p^{1-2x}\times p^{\frac{1}{2}}=q^{1-2x}\times q^{\frac{1}{2}}$

Now solving $x$ for $p$
$\Rightarrow 1-2x+\frac{1}{2}=0$
$\Rightarrow 2-4x+1=0$
$\Rightarrow -4x=-3$
$\Rightarrow x=\frac{3}{4}$

Now solving $x$ for $q$
$\Rightarrow 1-2x+\frac{1}{2}=0$
$\Rightarrow 2-4x+1=0$
$\Rightarrow -4x=-3$
$\Rightarrow x=\frac{3}{4}$

$\therefore L.H.S=R.H.S$

The given statement is true.