Question

Please Answer It.....​

Answer 1

$\color{red}\large\underline{\underline{Question:}}$

$x = 5 - 2\sqrt{6} ,\:then\:find\:x^{2} + \dfrac{1}{x^{2}}$

______________________________________

$\color{blue}\large\underline{\underline{To\:Find:}}$

$\underline{The\:value\:of\:the\:Equation}$

______________________________________

$\color{purple}\large\underline{\underline{We\:know:}}$

• $\dfrac{1}{x} = 5 + 2\sqrt{6}$
• $(a + b)^{2} = a^{2} + 2ab + b^{2}$
• $(a - b)^{2} = a^{2} - 2ab + b^{2}$

______________________________________

$\color{green}\large\underline{\underline{Solution:}}$

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

Putting the value of $\dfrac{1}{x} = 5 + 2\sqrt{6}$ in the equation , we get.

$\Rightarrow (5 - 2\sqrt{6})^{2} + (5 + 2\sqrt{6})^{2}$

$\Rightarrow (5^{2} - 20\sqrt{6} + 2\sqrt{6}^{2}) + (5^{2} + 20\sqrt{6} + 2\sqrt{6}^{2})$

$\Rightarrow (25 - 20\sqrt{6} + 24) + (25 + 20\sqrt{6} + 24)$

$\Rightarrow 25 - 20\sqrt{6} + 24 + 25 + 20\sqrt{6} + 24$

$\Rightarrow 25 + 24 + 25 + 24$

$\Rightarrow 98$

${\boxed{\therefore x^{2} + \dfrac{1}{x^{2}} = 98}}$