Question

if x=5+2√6 and y = 1/x,then find the value of x ^2+y^2​

Answer 1

Step-by-step explanation:

Given that

x = 5+2√6

y = 1/x

= 1/5+2√6

Take x^2 + y^2

Answer is continuous in photo

Answer 2

$x^{2}+y^{2}=98$

Explanation:

Here, $x=5+2\sqrt{6}$

Given: $y=\dfrac{1}{x}$

$\Rightarrow y=\dfrac{1}{5+2\sqrt{6}}$

$\Rightarrow y=\dfrac{5-2\sqrt{6}}{(5+2\sqrt{6})(5-2\sqrt{6})}$

$\Rightarrow y=\dfrac{5-2\sqrt{6}}{25-24}$; use $a^{2}-b^{2}=(a+b)(a-b)$

$\Rightarrow y=\dfrac{5-2\sqrt{6}}{1}$

$\Rightarrow y=5-2\sqrt{6}$

Now, $x^{2}+y^{2}$

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

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

$=98$