Question

x+1/x=4 then find the x^3+1/x^3=?​

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 4.

As we know that,

Formula of :

⇒ (x + y)³ = x³ + 3x²y + 3xy² + y³.

Using this formula in the equation, we get.

Cubing on both sides of the equation, we get.

⇒ (x + 1/x)³ = (4)³.

⇒ (x)³ + 3(x)²(1/x) + 3(x)(1/x)² + (1/x)³ = (4)³.

⇒ x³ + 3x + 3/x + 1/x³ = 64.

⇒ x³ + 1/x³ + 3(x + 1/x) = 64.

Put the values of (x + 1/x) = 4 in the equation, we get.

⇒ x³ + 1/x³ + 3(4) = 64.

⇒ x³ + 1/x³ + 12 = 64.

⇒ x³ + 1/x³ = 64 - 12.

⇒ x³ + 1/x³ = 52.

Answer 2

Given:-

(x+1)/x = 4

To Find:-

(x³+1)/x³ ••••(1)

Solution:-

(x+1)/x = 4

x+1 = 4x

4x - x = 1

3x = 1

x = 1/3

Substituting the value of x in equation (1), we get,

= [ (1/3)³+1 ] / (1/3)³

= [ (1+27)/27 ] / (1/27)

= (28×27)/27

= 28

Hence, the value of (x³+1)/x³ is 28.

Verification:-

LHS = (x+1)/x

= (1/3 + 1/1) / (1/3)

= [(1+3)/3] / (1/3)

= (4/3) / (1/3)

= (4 × 3) / 3

= 4 = RHS

Hence, verified!