Question

if (a+b)=2 and (a-b)=10 find the value of :(a2+b2) and ab

Answer 1

Step-by-step explanation:

a+b =2

a-b= 10 (by adding)

2a=12

2b= 8 (by subtracting)

2a+2b =20

a =6

b=4

ab =24

Answer 2

Correct Question :-

If a + b = 2, a - b = 10 then find the values of a² + b² and ab

Answer :-

The value of a² + b² is 52 and the value of ab is - 24.

Solution :-

We know that

(a + b)² = (a - b)² + 4ab

Here

• a + b = 2

• a - b = 10

By substituting the values

⇒ (2)² = (10)² + 4ab

⇒ 4 = 100 + 4ab

⇒ 4 - 100 = 4ab

⇒ - 96 = 4ab

⇒ - 96/4 = ab

⇒ - 24 = ab

⇒ ab = - 24

We know that

(a + b)² = a² + b² + 2ab

Here

• a + b = 2

• ab = - 24

By substituting the values

⇒ (2)² = a² + b² + 2(-24)

⇒ 4 = a² + b² - 48

⇒ 4 + 48 = a² + b²

⇒ 52 = a² + b²

⇒ a² + b² = 52

Therefore the value of a² + b² is 52 and the value of ab is - 24.