Question

if X=(2+√5) find the value of x in X×X+1/X×X

Answer 1

heya

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Given:

x= 2+√5

now,

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

now, substituting the value of x,

$= \frac{(2 + \sqrt{5})^{2} + 1 }{(2 + \sqrt{5} )^{2} } \\ \\ = \frac{4 + 5 + 4 \sqrt{5} + 1 }{9 + 4 \sqrt{5} } \\ \\ = \frac{10 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ = \frac{10 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \times \frac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5} } \\ \\ = \frac{90 - 40 \sqrt{5} + 36 \sqrt{5} - 80}{ {9}^{2} - (4 \sqrt{5})^{2} } \\ \\ = \frac{90 - 4 \sqrt{5} - 80 }{81 - 80} \\ \\ = 10 - 4 \sqrt{5}$
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i hope it helps you! :-)

Answer 2

Here is your answer