Question

If a-b = 6 and a^2+b^2=42, find the value of ab .

Answer 1

ITS HELP YOU


(a-b)²+2ab =42

(6)²+2ab = 42

36+2ab = 42

2ab = 42-36

ab = 6/2

ab = 3

I hope it's help and correct

Answer 2

Answer :-

ab = 3

Explanation :-

Given :-

a - b = 6

a² + b² = 42

To find :-

Value of ab

Solution :-

We know that

(a - b)² = a² + b² - 2ab

Here

• a - b = 6

• a² + b² = 42

By substituting the values

⇒ (6)² = 42 - 2ab

⇒ 36 = 42 - 2ab

Transpose - 2ab to LHS ( -2ab becomes + 2ab)

⇒ 36 + 2ab = 42

Transpose 36 to RHS (36 becomes - 36)

⇒ 2ab = 42 - 36

⇒ 2ab = 6

Transpose 2 to RHS (Multiplication becomes division)

⇒ ab = 6/2

⇒ ab = 3

Therefore the value of ab is 3.

Verification :-

(a - b)² = a² + b² - 2ab

⇒ (6)² = 42 - 2(3)

⇒ 36 = 42 - 6

⇒ 36 = 36

Identity used :-

• (a - b)² = a² + b² - 2ab