Question

Find the value of a² + b² if a-b = 5 and ab = 36​

Answer 1

Answer:

Step-by-step explanation:

Given that,

a - b = 9 and ab = 36

We know the formula

(a + b)² = (a - b)² + 4ab

On putting given values , We get

(a + b)² = 9² + 4×(36)

→ (a + b)² = 81 + 144

→ (a + b)² = 225

→ (a + b) = ±15

Now,

★ When

a - b = 9 and a + b = 15

→ a² - b² = (a + b) (a - b)

→ a² - b² = 15 × 9

→ a² - b² = 135

★ When

a - b = 9 and a + b = -15

→ a² - b² = (a + b) (a - b)

→ a² - b² = -15 × 9

→ a² - b² = -135

HENCE,

a² - b² = 135 or -135

Answer 2

Answer:

97

Step-by-step explanation:

Identity – (a-b)² = a² + b² - 2ab

Given, (a-b) = 5 and ab = 36

=> (5)² = a² + b² -2(36)

=> 25 = a² + b² - 72

=> 25 + 72 = a² + b²

=> a² + b² = 97