Question

Assertion (A): If `x + 1/x = 5, "then"  x^3 + 1/x^3 = 125`

Reason (R): `(x + 1/x)^3 = x^3 + 1/x^3 + 3(x + 1/x)`

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, but R is the incorrect reason for A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Assertion (A): If `x + 1/x = 5, "then"  x^3 + 1/x^3 = 125`

Reason (R): `(x + 1/x)^3 = x^3 + 1/x^3 + 3(x + 1/x)`

In the reason formula is correct, so let’s substitute values,

`(5)^3 = x^3 + 1/x^3 + 3(5)`

`125 = x^3 + 1/x^3 + 15`

`x^3 + 1/x^3 = 125 - 15`

`x^3 + 1/x^3 = 110`

Hence, the assertion is false, but the reason is true.