Question

if x+1/x=3,then find the value of x2+1/x²​

Answer 1

Answer:

$\frac{x^{2}+1}{x^{2}} = 5$

Step-by-step explanation:

Given, $\frac{x+1}{x}=3$

           $\frac{x+1}{x}=3 \\ \\ \frac{x+1}{x} \times x=3 \times x \\ \\ x+1 = 3x \\ \\ (x+1)-x=3x-x \\ \\ 1 = 2x \\ \\ x = \frac{1}{2}$

Therefore, $\frac{x^{2}+1}{x^{2}} =$

                 $\frac{(\frac{1}{2})^{2}+1}{(\frac{1}{2})^{2}} = \frac{\frac{1}{4}+1}{\frac{1}{4}} \\ \\ \frac{\frac{1}{4}+1}{\frac{1}{4}} = \frac{5}{4} \times \frac{4}{1} = 5$