Question

if x=7+3√5/7-3√5,then find the value of x2+1/x2​

Answer 1

Step-by-step explanation:

$x = \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } = \frac{{(7 + 3 \sqrt{5})}^{2} }{(7 - 3 \sqrt{5})(7 + 3 \sqrt{5})} =$

$\frac{49 + 45 +42 \sqrt{5}}{49 - 45} = \frac{94 + 42 \sqrt{5} }{4}$

$\frac{1}{x} = \frac{4}{94 + 42 \sqrt{5} } = \frac{4(94 - 42 \sqrt{5})}{(94 + 42 \sqrt{5})(94 - 42 \sqrt{5})} =$

$\frac{4(94 - 42 \sqrt{5})}{ {94}^{2} - 42 \times 42 \times 5} = \frac{4(94 - 42 \sqrt{5})}{8836 - 8820} = \frac{4(94 - 42 \sqrt{5})}{16}$

$= \frac{94 - 42 \sqrt{5} }{4}$

$x + \frac{1}{x} = \frac{94 + 42 \sqrt{5} }{4} + \frac{94 - 42 \sqrt{5} }{4} = \frac{188}{4} =$

$47$

Hence square on both sides we get

${(x + \frac{1}{x})}^{2} = {47}^{2} = > {x}^{2} + \frac{1}{ {x}^{2} } + 2.x. \frac{1}{x}$

$= 2209 = > {x}^{2} + \frac{1}{ {x}^{2}} = 2207$

Hope it helps you.

Answer 2

Answer:

hey mate

ur answer is in the attachment above.

Hope it helps

Please mark it as a brainliest