Question

If a-b =7 and ab =8 evaluate i)a²+b² and ii)a+b​

Answer 1

Answer:

Take the square of both equations.

(a+b) ² =(8) ²

a ² + b² + 2ab =64 (equation 1)

(a-b) ² = (6)²

a² + b² - 2ab = 36 (equation 2)

Now add equation 1 with equation 2

(a ² + b² + 2ab) + (a² + b² - 2ab) = 64 + 36

2a² + 2b² = 100

2(a² + b²) = 100

a² + b² = 50

Answer 2

(a-b)²= a²-2ab+b²

a-b =7,ab =8

7²=-2(8)+a²+b²

a²+b²=49+16

a²+b²=65

(a+b)²= a²+2ab+b²

(a+b)²=16+65

(a+b)²=81

a+b=9