Question

(a-b)=2 and (a+b)=10 find the value of (a^2+b^2)​

Answer 1

Answer:

           52

Step-by-step explanation:

Method 1 - Solve for a and b then calculate a²+b²

a-b = 2

a+b = 10

Adding these equations gives

2a = 12  ⇒  a = 6

and

b = 10 - a = 10 - 6 = 4.

So  a² + b² = 6² + 4² = 36 + 16 = 52

Method 2 - Calculate a²+b² directly without finding a and b

2(a² + b²) = (a² + 2ab + b²) + (a² - 2ab + b²) = (a+b)² + (a-b)² = 10² + 2² = 104

⇒  a² + b² = 104/2 = 52

Hope that helps