Question

if a-b = 5 and a²-b² = 65, then find the value of a²+b²​

Answer 1

Answer:

a²+b² =97

Step-by-step explanation:

(a-b) =5

a²-b² =65

a²-b² = (a+b) * (a-b)

65 = (a+b) * 5

(a+b) = 65/5

(a+b) = 13

(a+b)² = 13² = 169

(a+b)² = a²+b² + 2ab

(a-b) =5² = 25

(a-b)² = a²+b² - 2ab

(a+b)² - (a-b)² = 169 - 25 = 144

(a+b)² - (a-b)² = a²+b² + 2ab - (a²+b² - 2ab)

(a+b)² - (a-b)² = 4ab

144 = 4ab

ab= 144/4 = 36

(a+b)² = a²+b² + 2ab

169 = a²+b² + 2(36)

169 = a²+b² + 72

a²+b² = 169-72

a²+b² =97