Question

if x plus one upon x is equal to root 5 find the value of x power 4 + 1 upon x ki power 4

Answer 1

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$x + \frac{1}{x} = \sqrt{5} \\ {(x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} \\ {( \sqrt{5}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ 5 = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3 \\ {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } \\ {(3)}^{2} = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ 9 = {x}^{4} + \frac{1}{ {x}^{4} } + 2 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 7$
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Answer 2

Answer: 7

Step-by-step explanation:

as we know

if $x+\frac{1}{x}=a$

then $x+\frac{1}{x}=a\\\\ x^{4}+\frac{1}{x^{4}}=a^{4}-4a^{2}+2\\\\=(\sqrt{5})^{4}-4(\sqrt{5})^{2}+2\\\\=25-4*5+2\\\\=25-20+2\\\\=7$