Question

if (x^2 - 1/x^2) = 18, find value of x^3-1/x^3

Answer 1

18x^3-1 is the answer

Answer 2

Step-by-step explanation:

◢Given:-

x^2+1/x^2 = 18

◢To find:

Find the value of x^3-1/x^3 ?

◢Solution:-

Given that,

x^2+1/x^2 = 18 --------------------(1)

We know that

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

=> a^2+b^2 = (a-b)^2+2ab

Where, a = x^2 and b = 1/x^2

=> x^2+(1/x^2) = [x-(1/x)]^2+2(x)(1/x)

=> 18 = [x-(1/x)]^2+2

=> [x-(1/x)^2 = 18-2

=> [x-(1/x)]^2 = 16

=> x - (1/x) = √16

=> x - (1/x) = 4 --------------------------(2)

(On taking positive value)

Now,

The value of x^3-(1/x^3)

We know that

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

Where a = x and b = 1/x

=> x^3 - (1/x)^3 = [x-(1/x)][x^2+(x)(1/x)+(1/x)^2]

=> x^3 - (1/x)^3 = [x-(1/x)][x^2+1+(1/x)^2]

=> x^3 - (1/x)^3 = [x-(1/x)][x^2+(1/x)^2+1]

=> x^3 - (1/x)^3 = (4)(18+1)

=> x^3 - (1/x)^3 = 4(19)

=> x^3 - (1/x)^3 = 76

Answer:-

The value of x^3 - (1/x)^3 for the given problem is 76

Used Formulae:-

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

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

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

• Hope it's help you..☺