Question

if x cube minus one upon x cube is equal to 14 find the value of x minus one upon x​

Answer 1

Let (x - 1/x) = p Cubing on both sides of the equation, (x - 1/x)3 = p3 x3 - 1/x3 - 3(x - 1/x) = p3 (14) - 3p = p3 [Given that x3 - 1/x3 = 14] p3 + 3p - 14 = 0 (p - 2) is a factor of (p3 + 3p - 14) as p(2) = 0. [According to remainder theorem] Therefore the other factor of (p3 + 3p - 14) on dividing by (p - 2) is (p2 + 2p + 7). ⇒ (p - 2)(p2 + 2p + 7) = 0 ⇒ p = 2 The other values of p are not real numbers as (p2 + 2p + 7) can not be factored. Therefore, (x - 1/x) = 2.

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Answer 2

Answer:

Step-by-step explanation:

2 is the right answer. The steps are given above