Question

Sabendo que a²+b²=25 e que ab= -8, dê o valor de (2a-b)².

Answer 1

Resposta:

(2a-b)²=64

Explicação passo-a-passo:

(2a-b)²=4a²-4ab+b²

a²+b²=25

ab=-8

2ab=-16

4a²b²=256

4a²=256/b²

4a²-4ab+b²

256/b² -32 +b² = 0

b⁴ -32b² +256 = 0

b²=x

x²-32x+256=0

Δ=1024-1024=0

x=32/2

x=16

b²=16

b=±4

ab=-8

4a=-8

a=-2

-4a=-8

a=2

(2.2-(-4))²=(4+4)²=(8)²=64

(2.(-2)-4)²=(-4-4)²=(-8)²=64