Question

If (a + b) = 2 and (a - b) = 10, find the values of : (i) (a² + b²) (ii) ab.​

Answer 1

Answer:

52 & - 24

Step-by-step explanation:

Square on both sides of (a + b) and (a - b), then add both:

→ (a + b)² + (a - b)² = 2² + 10²

→ (a² + b² + 2ab)+(a² + b² - 2ab) = 4+100

→ a² + b² + 2ab + a² + b² - 2ab = 104

→ 2(a² + b²) = 104

→ a² + b² = 52

Square on both sides of a + b:

→ (a + b)² = 2²

→ a² + b² + 2ab = 4

→ 52 + 2ab = 4 {a²+b²=52}

→ 2ab = 4 - 52 = - 48

→ ab = (-48/2)

→ ab = - 24

Answer 2

(a+b)² = a² + b² + 2ab

and

(a-b)² = a² + b² - 2ab

now

(a+b)² - (a-b)² = 4ab

put the value of a+b =2 and a-b =10

2² - 10² = 4ab

ab = -96/4

(I) ab = -24

Again

(a+b)² + (a-b)² = 2(a²+b²)

2² + 10² = 2 (a²+b²)

a² + b² = 104/2

(ii) a² + b² = 52