Question

if x³- 1/x³=14, then x-1/x =
a)2
b)3
c)4
d)5​

Answer 1

Answer:

the answer is 2

Step-by-step explanation:

Given

x^3 - 1/x^3 = 14

And you that (a-b)^3 = a^3 -b^3 -3ab (a - b)…(1)

So according to equation (1) you will have

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

=> (x - 1/x)^3 + 3( x-1/x) - 14 = 0………..(2)

Let m = (x - 1/x) so putting the value of m in equation (2) you will get

m^3 + 3m - 14 = 0 ……..(3)

By hit and trail on putting m = 2 you will find that it is the root of the above equation (3)

So dividing equation (3) by (m-2) you will get

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

Since the discrimnant of the quadratic equation is less than zero so it will not have any real soution.

Hence, m-2 = 0

=> m = 2

So ( x-1/x ) = 2 ans.