Question

1) a^2+2ab+b^2=25, find a+b

All values of a+b are...

2) a^2−8ab+16b^2=81, find a–4b

All values of a-4b are...

Answer 1

1) -5 and +5; 2) -9 and +9

Explanation:

1) a² + 2ab + b² = 25

(a + b)² = 25 Wrote the left-hand side as a square

a + b = ±5 Took the square root of each side

All values of a + b are -5 and +5.

2) a² − 8ab + 16b² = 81

(a - 4b)² = 81 Wrote the left-hand side as a square

a - 4b = ±9 Took the square root of each side

All values of a - 4b are -9 and +9.