Question

28. If a + b = 10 and ab = -10, then find the value of a + b2.​

Answer 1

Correct Question :-

If a + b = 10 and ab = -10, then find the value of a² + b²

Answer :-

a² + b² = 110

Solution :-

We know that

(a + b)² = a² + b² + 2xy

⇒ (a + b)² - a² - b² = 2ab

⇒ (a + b)² - (a² + b²) = 2ab

Here a + b = 10

ab = - 10

By substituting the values

⇒ (10)² - (a² + b²) = 2(-10)

⇒ 100 - (a² + b²) = - 20

⇒ - (a² + b²) = - 20 - 100

⇒ - (a² + b²) = - 120

⇒ a² + b² = - ( - 120 )

⇒ a² + b² = 120

Therefore value of a² + b² is 120

Verification :-

(a + b)² - (a² + b²) = 2ab

⇒ (10)² - (120) = 2(-10)

⇒ 100 - 120 = - 20

⇒ - 20 = - 20

Identity used :-

• (a + b)² - (a² + b²) = 2ab