Question

if p + 1/p = 12 , find the value of p - 1 / p​

Answer 1

Answer:

The answer is $\sqrt{140}$

Step-by-step explanation:

Given

 $p+\frac{1}{p}=12\Rightarrow (p+\frac{1}{p})^2=12^2\\\Rightarrow p^2+\frac{1}{p^2}+2p\times \frac{1}{p}=144\\\Rightarrow p^2+\frac{1}{p^2}+2=144\\\therefore p^2+\frac{1}{p^2}=144-2=142$

Let $p-\frac{1}{p}=x$

$\Rightarrow x^2=(p-\frac{1}{p})^2=p^2+\frac{1}{p^2}-2p\times \frac{1}{p}$

         $=p^2+\frac{1}{p^2}-2=142-2=140$

$\therefore x=\sqrt{140}=2\sqrt{35}$