Question

If (a + b) = 2 and (a - b) = 10 then the value of (a2 + b2 )​

Answer 1

Answer:

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

Step-by-step explanation:

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.

Answer 2

Answer:

52

Step-by-step explanation:

(a+b) = 2 ---------(1)

(a-b) = 10 ------------(2)

now add 1 and 2

a + b = 2

a - b = 10

---------------

=} 2a = 12

a = 12/2

a = 6

now substitute a=6 in 1

=} a+b = 2

=} 6+b=2

=} b= 2-6

=}b= -4

substitute both a and b in (a^2 + b^2)

=} (6)^2 + (-4)^2

=} 36 + 16

=} 52

hope it helped

have a good day