Question

Assertion: x + y = 8, xy = 15 then x² + y² = 34

Reason: x² + y² – 2xy = (x – y)²

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is true but Reason (R) is false.

Explanation:

Assertion (A) states: If x + y = 8 and xy = 15, then x² + y² = 34.

Using the identity:

(x + y)² = x² + 2xy + y² 

Substituting:

8² = x² + 2 × 15 + y²

⇒ 64 = x² + 30 + y²

Thus, x² + y² = 64 – 30 = 34.

Therefore, the assertion is true.

Reason (R) states: x² + y² – 2xy = (x – y)².

This is a true identity but it does not explain why x² + y² = 34 based on the given x + y and xy. 

The assertion was derived using the identity (x + y)² = x² + 2xy + y², not from the identity given in the reason.

Hence, the assertion is true, the reason is true, but the reason is not the correct explanation for the assertion.