Question

if x+1/x=4 then prove x2-1/x2=192​

Answer 1

Answer:

This is false.

Step-by-step explanation:

$\dfrac{x+1}{x}=4\\\\\dfrac{x+1}{x}=\dfrac{4}{1}\qquad|\text{cross multiply}\\\\4x=x+1\qquad|\text{subtract}\ x\ \text{from both sides}\\\\3x=1\qquad|\text{divide both sides by 3}\\\\x=\dfrac{1}{3}$

Substitute it to

$\dfrac{x^2-1}{x^2}$

$\dfrac{\left(\frac{1}{3}\right)^2-1}{\left(\frac{1}{3}\right)^2}=\dfrac{\frac{1}{9}-1}{\frac{1}{9}}=\dfrac{\frac{1}{9}-\frac{9}{9}}{\frac{1}{9}}=\dfrac{1-9}{9}:\dfrac{1}{9}=-\dfrac{8}{9}\cdot\dfrac{9}{1}=-\dfrac{8}{1}\cdot\dfrac{1}{1}=-8\neq192$