Question

If x minus one by X is equals to 3 then find the value of x cube minus one by x cube

Answer 1

x-(1/x)=3

and we have to find x³-(1/x³)

solution:

we know rhat,

(a-b)³=a³-b³-3ab(a-b)

here a=x and b=1/x

(x-1/x)³=x³-1/x³-3*x*1/x(x-1/x)

given (x-1/x)=3

therefore,

(3)³=x³-1/x³-3(3)

27=x³-1/x³-9

27+9=x³-1/x³

36=x³-x/x³

answer is 36

hope you understood

Answer 2

Given:

$x-\frac{1}{x}=3$

To Find:

The value of $x^3-\frac{1}{x^3}$

Solution:

Before solving we need to know an algebraic identity and also need to calculate certain values required due to the identity

The identity is

$a^3-b^3=(a-b)(a^2+b^2+ab)$

Now we use this formula to simplify the given equation

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

before proceeding further need to find the value of $x^{2} +\frac{1}{x^2}$

using the given value we will derive this value

$(x-\frac{1}{x})^2=x^{2} +\frac{1}{x^2} -2\\9=x^2+\frac{1}{x^2} -2\\ x^2+\frac{1}{x^2}=11$

Now putting all the values in the identity form

$x^3-\frac{1}{x^3} =(x-\frac{1}{x} )(x^2+\frac{1}{x^2} +1)\\\\=3(11+1)\\=3*12\\=36$

Hence, the value of x cube minus one by x cube is 36.