Question

if x=3+√8 ,then find the value ofx²+1/x²​

Answer 1

Step-by-step explanation:

= (3 + root 8)^2 + 1 / (3+ root 8)^2

= 9 + 8+ 1 / 17

= 18 / 17

Answer 2

Step-by-step explanation:

$x = 3 + \sqrt{8} \\ \\ {x}^{2} = {(3 + \sqrt{8}) }^{2} \\ \\ {x}^{2} = 9 + 8 + 6 \sqrt{8} \\ \\ {x}^{2} = 17 + 6 \sqrt{8} \\ \\ {x}^{2} = 17 + 12 \sqrt{2} ...equation(1) \\ \\ {x}^{4} = {(17 + 12 \sqrt{2} )}^{2} \\ \\ {x}^{4} = 289 + 288 + 408 \sqrt{2} \\ \\ {x}^{4} = 577 + 408 \sqrt{2} ...equation(2) \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = \frac{ {x}^{4} + 1}{ {x}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{577 + 408 \sqrt{2} + 1}{17 + 12 \sqrt{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{578 + 408 \sqrt{2} }{17 + 12 \sqrt{2} }</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>\</strong><strong>:</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>=</strong><strong> </strong><strong> </strong><strong>\</strong><strong>f</strong><strong>r</strong><strong>a</strong><strong>c</strong><strong>{</strong><strong>3</strong><strong>4</strong><strong>(</strong><strong>1</strong><strong>7</strong><strong>+</strong><strong>1</strong><strong>2</strong><strong> </strong><strong>\</strong><strong>s</strong><strong>q</strong><strong>r</strong><strong>t</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>)</strong><strong>}</strong><strong>{</strong><strong>1</strong><strong>7</strong><strong>+</strong><strong>1</strong><strong>2</strong><strong> </strong><strong>\</strong><strong>s</strong><strong>q</strong><strong>r</strong><strong>t</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong> </strong><strong>}</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>=</strong><strong> </strong><strong>3</strong><strong>4</strong><strong>$