Question

If [x^8 + 1/x^8]=47, what is the value of [x^6 + 1/x^6]
?
(a) 36
(b) 27
(c) 18
(d) 9

Answer 1

Answer:

c

Step-by-step explanation:

In this question fist you take common x^8

after this you have to take 4 root and solve you will get 1/x^6 answer and ther you you have to put this value in second equation and then you will get answers

Answer 2

The value of  $x^{6} + \frac{1}{x^{6} }$ is 18

Step-by-step explanation:

Given : $x^{8} + \frac{1}{x^{8} } =47$

To find: $x^{6} + \frac{1}{x^{6} }$

Formula used: $(a + \frac{1}{a} )^{2} = P$

Solution:

$x^{8} + \frac{1}{x^{8} } =47$

Add 2 on both sides,

$x^{8} + \frac{1}{x^{8} } + 2=47 +2$

$(x^{4} )^{2} + \frac{1}{(x^{8})^{2} }+ 2(x^{4} )\frac{1}{x^{4} } =49$

$x^{4} + \frac{1}{x^{4} } + 2 = 7 + 2$

$x^{4} + \frac{1}{x^{4} } + 2 = 9$

$x^{2} + \frac{1}{x^{2} } = 3$

Taking cube on both sides

$(x^{2} +\frac{1}{x^{2} } )^{3} = 3^{3}$

$x^{6} +\frac{1}{x^{6} } + 3 (x^{2}) (\frac{1}{x^{2} } )(x^{2} +\frac{1}{x^{2} } ) = 27$

$x^{6} + \frac{1}{x^{6} } + 3(3) = 27$

$x^{6} + \frac{1}{x^{6} } = 27 - 9$

$x^{6} + \frac{1}{x^{6} } = 18$

Final answer:

The value of  $x^{6} + \frac{1}{x^{6} }$ is 18

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