Calculati:a)(x-1)^2=1 b)x^2-1=1 c)x^2+6x+9=16 d)(x+2)^2-4=0 e)2x+3 supra 3=9 supra 2x-3

[tex]a) {(x - 1)}^{2} = 1[/tex]

[tex] {x}^{2} - 2x + 1 = 1[/tex]

[tex] {x}^{2} - 2x + 1 - 1 = 0[/tex]

[tex] {x}^{2} - 2x = 0[/tex]

[tex]x(x - 2) = 0[/tex]

[tex] = > x_{1} = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex] = > x_{2} = 2[/tex]

[tex]b) {x}^{2} - 1 = 1[/tex]

[tex] {x}^{2} = 1 + 1[/tex]

[tex] {x}^{2} = 2[/tex]

[tex]x = \pm \sqrt{2} [/tex]

[tex]x_{1}=\sqrt{2}[/tex]

[tex]x_{2}=-\sqrt{2}[/tex]

[tex]c) {x}^{2} + 6x + 9 = 16[/tex]

[tex] {(x + 3)}^{2} = 16[/tex]

[tex]x + 3 = \pm \sqrt{16} [/tex]

[tex]x+3=\pm4[/tex]

[tex]1)x + 3 = 4 [/tex]

[tex]x = 4 - 3[/tex]

[tex]x_{1} = 1[/tex]

[tex]2)x + 3 = -4 [/tex]

[tex]x = - 4 - 3[/tex]

[tex]x_{2} = - 7[/tex]

[tex]d) {(x + 2)}^{2} - 4 = 0[/tex]

[tex] {(x + 2)}^{2} = 4[/tex]

[tex]x + 2 = \pm \sqrt{4} [/tex]

[tex]x + 2 = \pm2[/tex]

[tex]1)x + 2 = 2[/tex]

[tex]x = 2 - 2[/tex]

[tex]x_{1} = 0[/tex]

[tex]2)x + 2 = - 2[/tex]

[tex]x = - 2 - 2[/tex]

[tex]x_{2} = - 4[/tex]

[tex]e) \frac{2x + 3}{3} = \frac{9}{2x - 3} [/tex]

[tex](2x + 3)(2x - 3) = 3 \times 9[/tex]

[tex] {4x}^{2} - 9 = 27[/tex]

[tex]4 {x}^{2} = 27 + 9[/tex]

[tex]4 {x}^{2} = 36 \: | \div 4[/tex]

[tex] {x}^{2} = 9[/tex]

[tex]x = \pm \sqrt{9} [/tex]

[tex]x = \pm3[/tex]

[tex]x_{1} = 3[/tex]

[tex]x_{2} = - 3[/tex]