Question

X-1÷x=5 find x square+1÷x square

Answer 1

Answer:

$\large \underline{\boxed{\boxed{\bold{\sf{x^2 + (\dfrac{1}{x})^2 = \boxed{\boxed{27}}}}}}}$

Step-by-step explanation:

$\textbf{Question: If x - \dfrac{1}{x} = 5 , find x^2 + (\dfrac{1}{x})^2 .}\\\\\\\textbf{Soluion:-}\\\\Given: x - \dfrac{1}{x} = 5.\\\\\text{Squaring both sides, we have}\\\\(x - \dfrac{1}{x})^2 = 5^2\\\\\\\implies x^2 + (\dfrac{1}{x})^2 - 2(x)(\dfrac{1}{x}) = 25\\\\\\\implies x^2 + (\dfrac{1}{x})^2 - 2 = 25\\\\\\\implies x^2 + (\dfrac{1}{x})^2 = 25 + 2 = 27\\\\\\\implies \large \underline{\boxed{\boxed{\bold{\sf{x^2 + (\dfrac{1}{x})^2 = \boxed{\boxed{27}}}}}}}$