Question

e) (x-5)²=1

f) (x-3)x²=-2x²

g) x²-3=4+2

Answer 1

Explicação passo-a-passo:

$(x - 5) {}^{2} = 1 \\ x {}^{2} - 10x + 25 = 1 \\ x {}^{2} - 10x + 25 - 1 = 0 \\ x {}^{2} - 10x + 24 = 0$

∆=b²-4ac

∆=(-10)²-4.1.24

∆=100-96

∆=4

$x = \frac{ 10 + \sqrt{4} }{2 \times 1} \\ x = 5 + 2 \\ x = 7 \\ \\ x = \frac{10 - \sqrt{4} }{2} \\ x = 5 - 2 \\ x = 3$

$(x - 3)x {}^{2} = - 2x {}^{2} \\ x {}^{3} - 3x {}^{2} = - 2x {}^{2} \\ x {}^{3 } - 3x {}^{2} + 2x {}^{2} = 0 \\ x {}^{3} - x {}^{2} = 0 \\ x {}^{2} (x - 1) = 0 \\ x {}^{2} = 0 \\ \\ x - 1 = 0 \\ x = + 1 \\ \\ x = 0$

$x {}^{2} - 3 = 4 + 2 \\ x {}^{2} = 4 + 2 + 3 \\ x {}^{2} = 9 \\ x = \sqrt{9} \\ x = 3 \\ x = - 3$