Question

The equation `sqrt(15 - 2x) = x`.

Assertion (A): x = 3. 

Reason (R): `sqrt(15 - 2x) = x` ⇒ 15 − 2x = x²

⇒ x² + 2x − 15 = 0 

⇒ x = −5 or x = 3

Options

• A is true, R is false.

• A is false, R is true.

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

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

Answer 1

A is true, R is false.

Explanation:

Given,

⇒ `sqrt(15 - 2x) = x`

⇒ 15 − 2x = x²

⇒ x² + 2x −15 = 0

⇒ x² + 5x − 3x − 15 = 0

⇒ x(x + 5) −3(x + 5) = 0

⇒ (x + 5)(x − 3) = 0

⇒ (x + 5) = 0 or (x − 3) = 0

⇒ x = −5 or x = 3

The quadratic equation mentioned in the reason is x² − 2x − 15 = 0 whereas the correct quadratic equation is x² + 2x − 15 = 0.

∴ Reason (R) is false.

Solution shows that one of the roots is 3.

∴ Assertion (A) is true.