Question

4) If x-1/x=5, fand the value of x²+ 1/x²​

Answer 1

Given:

$\sf x\ -\ \dfrac{1}{x}\ =\ 5$

To find:

$\sf The\ value\ of\ x^2\ +\ \dfrac{1}{x^2}.$

Answer:

$\sf x\ -\ \dfrac{1}{x}\ =\ 5$

Let's square the above expression.

$\sf \bigg(x\ -\ \dfrac{1}{x}\bigg)^2\ =\ 5^2$

According to the identities, (a - b)² = a² - 2ab + b². Using the same logic for the expression above,

$\sf x^2\ -\ 2\ \times\ x\ \times\ \dfrac{1}{x}\ +\ \dfrac{1}{x^2}\ =\ 25\\\\\\x^2\ -\ 2\ +\ \dfrac{1}{x^2}\ =\ 25\\\\\\x^2\ +\ \dfrac{1}{x^2}\ =\ 25 + 2\\\\\\x^2\ +\ \dfrac{1}{x^2}\ =\ 27$

Therefore, the value of x² + 1/x² is 27.