Question

me ajudem por favor​

Answer 1

1) x²-10x+25=0

(x-5)²=0

x-5=0

x=5 → letra a

2)2x²-10-8x=0

2x²-8x-10=0 ÷(2)

x²-4x-5=0

x²+x-5x-5=0

x(x+1)-5(x+1)=0

(x+1)(x-5)=0

x+1=0

x=1

x-5=0

x=5

letra a

3)0,1x²-0,7x+1=0 ×(10)

x²-7x+10=0

x²-2x-5x+10=0

x(x-2)-5(x-2)=0

(x-2)(x-5)=0

x-2=0

x=2 → letra d

4)

$\frac{x - 2}{3x} + \frac{2x - 1}{2} = \frac{5x + 2}{6} \\ \frac{2x - 4 + 6 {x}^{2} - 3x = 5 {x}^{2} + 2x }{6x} \\ 6 {x}^{2} - {5x}^{2} - 3x - 4 = 0$

x²-3x-4=0

x²+x-4x-4=0

x(x+1)-4(x+1)=0

(x+1)(x-4)=0

x+1=0

x=-1

x-4=0

x=4

Letra b

5)

$x(1 - x) = \frac{1}{4} \\ 4x(1 - x) = 1 \\ - 4 {x}^{2} + 4x - 1 = 0 \times ( - 1) \\ 4 {x}^{2} - 4x + 1 = 0$

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

Letra b

6)

$\frac{x - 3}{2} + \frac{1}{x} = - 3 \\ \frac{ {x}^{2} - 3x + 2 = - 6x }{2x} \\ {x}^{2} + 3x + 2 = 0$

x²+x+2x+2=0

x(x+1)+2(x+1)=0

(x+1)(x+2)=0

x+1=0 → x=-1

x+2=0 → x=-2

x²=4 ou x²=1

Letra d.

7)

$x + \frac{5}{x - 5} = 5 + \frac{5}{x - 5} \\ \frac{ {x}^{2} - 5x + 5 = 5x - 25 + 5 }{x - 5} \\ {x}^{2} - 5x - 5x + 25 = 0$

x²-10x+25=0

(x-5)²=0

x-5=0

x=5 letra a

8)2x²-2x+1=0

∆=4-8=-4<0

s=∅

Letra a

9)

$\frac{ {x}^{2} + 28 }{6} = \frac{7x}{3} - \frac{x}{2} \\ \frac{ {x}^{2} + 28 = 14x - 3x }{6} \\ {x}^{2} - 11x + 28 = 0$

$s = - \frac{b}{a} = - \frac{( - 11)}{1} = 11$

10)

$x + 1 = \frac{1}{x} \\ \frac{ {x}^{2} + x = 1}{x} \\ {x}^{2} + x - 1 = 0$

Letra b