Question

(i) lf x – y = 2 and x² + y² = 34 then xy = 15

(ii) (a + b)² = a² + 2ab + b²

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i) Given: x – y = 2 and x² + y² = 34.

Using the identity:

(x – y)² = x² + y² – 2xy

Substitute the given values:

2² = 34 – 2xy 

⇒ 4 = 34 – 2xy

⇒ 2xy = 34 – 4

⇒ 2xy = 30

⇒ xy = 15

So, the statement (i) xy = 15 is true.

(ii) The algebraic identity:

(a + b)² = a² + 2ab + b²

This is a standard identity and is always true.

However, the question asks if (ii) here is a conclusion or statement given just from the question without further condition; since it is a known algebraic identity, it is always true.

So, statement (ii) is true by the algebraic identity.

But from the context of the question, since (i) is verified based on given conditions and (ii) is universally true, both statements are true.

Therefore, the correct answer should be Both (i) and (ii).