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-1/5=8/x find x please ​

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x^3-1/x^3 =14 then find x-1/x . Please solve this problem

MathematicsAsked by Pranit Singh, a year ago

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( 1 Answers )

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Faisal

a year ago

( x - 1/x )^3 = x^3 - 1/x^3 - 3( x -1/x )

We know that x^3 - 1/x^3 = 14.

Let x - 1/x = a

Thus the equation is

a^3 = 14 - 3a

a^3 + 3a - 14=0 [ Cubic polynomial, find zeroes by factor theorem]

(a-2) (a^2 +2a + 7) = 0

Therefore (a-2) and (a^2 +2a +7) are factors of [ a^3 +3a - 14 =0 ]

Since (a^2 + 2a - 14) has no real roots , so only ( a=2 ) is zero of [ a^3 + 3a -14 =0 ]

Thus x - 1/x = 2 [ Final Answer ]