Question

If (x+1/x)=7find value of (x^2+1/x^2) and (x^4+1/x^4)

Answer 1

Answer:

x + 1 x = 7

⇒ (x + 1 x )2 =(7)2

⇒ (x2+  1 x 2 + 2) = 49

⇒ x2+  1 x 2 = 47

Therefore, x2+  1 x 2 = 47.

Step-by-step explanation:

Answer 2

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Here is your answer
$(x + \frac{1}{x} ) {}^{2} = 7 {}^{2} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 49 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 49 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 49 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 47$
Now

$( {x}^{2} + \frac{1}{ {x}^{2} } ) {}^{2} = (47) {}^{2} \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 2209 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 2209 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 2209 - 2 \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } = 2207$

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