Question

If x cube + 1 upon x cube equals to M and X square plus one upon x square equals to 47 find the value of m

Answer 1

x2 + 1/x2 = 83

x2 + 1/x2 - 2 = 83 - 2

(x - 1/x)2 = 81

(x - 1/x)2 = 92

x - 1/x = +/- 9

Now,

(x - 1/x)3 = +/- 93

x3 - 1/x3 - 3*x*1/x (x - 1/x) = +/- 729

Now, substituting the value of x - 1/x, we get,

x3 - 1/x3 - 3*9 = 729 and x3 - 1/x3 + 3*9 = -729

x3 - 1/x3 - 27 = 729 and x3 - 1/x3 + 27 = -729

x3 - 1/x3 = 756 and x3 - 1/x3 = -756

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Answer 2

Answer:

Hi ,

x² + 1/x² = 34----( 1 )

x² + 1/x² + 2 × x² × 1/x² = 34 +2

( x + 1/x )² = 36

( x + 1/x ) = √36

x + 1/x = 6 -----( 2 )

( x + 1/x )³ = x³ + 1/x³ + 3 ( x + 1/x )

6³ = x³ + 1/x³ + 3 × 6

216 = x ³ + 1/x³ + 18

216 - 18 = x³ + 1/x³

Therefore ,

x³ + 1/x³ = 198

I hope this helps you.

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