If a = 10 and b = 2, what are the values of (a + b)² and a² + b²? (a + b)² = (10 + 2)² = 12² = 144 Class 9

If a = 10 and b = 2, what are the values of (a + b)² and a² + b²? (a + b)² = (10 + 2)² = 12² = 144 Class 9

Question 1.

If a = 10 and b = 2, what are the values of

(a + b)² and a² + b²?

(a + b)² = (10 + 2)² = 12² = 144 and

a² + b² = 10² + 2² = 104.

So, in this case, (a + b)² > a² + b²

But is it true for all numbers a and b? Class 9

Answer:

No

Let a = -1 and b = 2

(a + b)² = (-1 + 2)² = 1² = 1

a² + b² = (-1)² + 2² = 1 + 4 = 5

Question 2.

What can you say about a and b if (a + b)² < a² + b² ? Class 9

Answer:

Using identity:

(a + b)² = a² + 2ab + b²

If (a + b)² < a² + b², then

a² + 2ab + b² < a² + b² ⇒ 2ab < 0

So, ab is negative, meaning a and b have opposite signs (one positive, one negative).