Question

(e) If a² + b² = 13 and ab = 6, find the value of (i) (a+b)² (ii) (a−b)²​

Answer 1

Answer: Given a² + b² = 13 and ab = 6, we need to find (i) (a+b)² and (ii) (a−b)².

(i) (a+b)²

We can use the identity:

(a+b)² = a² + 2ab + b²

We know that a² + b² = 13 and ab = 6, so we can substitute these values into the identity to get:

(a+b)² = a² + 2ab + b²

= 13 + 2(6)

= 25

Therefore, (a+b)² = 25.

(ii) (a−b)²

We can use the identity:

(a-b)² = a² - 2ab + b²

Again, we know that a² + b² = 13 and ab = 6, so we can substitute these values into the identity to get:

(a-b)² = a² - 2ab + b²

= 13 - 2(6)

= 1

Therefore, (a−b)² = 1.

To summarize:

(a+b)² = 25

(a−b)² = 1

Explanation: