[tex]3)a)3 {x}^{2} = 70[/tex]
[tex] {x}^{2} = \frac{70}{3} [/tex]
[tex]x = \pm \sqrt{ \frac{70}{3} } [/tex]
[tex]x = \pm \frac{ \sqrt{70} }{ \sqrt{3} } [/tex]
[tex]x = \pm \frac{ \sqrt{210} }{3} [/tex]
[tex]b) \frac{x}{2} = \frac{8}{x} [/tex]
[tex] {x}^{2} = 16[/tex]
[tex]x = \pm \sqrt{16} [/tex]
[tex]x = \pm4[/tex]
[tex]c) \frac{3x}{5} = \frac{20}{3x} [/tex]
[tex]9 {x}^{2} = 100[/tex]
[tex] {x}^{2} = \frac{100}{9} [/tex]
[tex]x = \pm \sqrt{ \frac{100}{9} } [/tex]
[tex]x = \pm \frac{ \sqrt{100} }{ \sqrt{9} } [/tex]
[tex]x = \pm \frac{10}{3} [/tex]
[tex]d) {(x + 3)}^{2} = 25[/tex]
[tex]x + 3 = \pm \sqrt{25} [/tex]
[tex]x + 3 = \pm5[/tex]
[tex]1)x + 3 = 5 = > x = 5 - 3 = 2[/tex]
[tex]2)x + 3 = - 5 = > x = - 5 - 3 = - 8[/tex]
[tex]e) {(3x - 1)}^{2} = 49[/tex]
[tex]3x - 1 = \pm \sqrt{49} [/tex]
[tex]3x - 1 = \pm7[/tex]
[tex]1)3x - 1 = 7 = > 3x = 7 + 1 = > 3x = 8 = > x = \frac{8}{3} [/tex]
[tex]2)3x - 1 = - 7 = > 3x = - 7 + 1 = > 3x = - 6 = > x = - \frac{6}{3} = > x = - 2[/tex]
[tex]f) {x}^{2} + 4x + 4 = 16[/tex]
[tex] {x}^{2} + 4x + 4 - 16 = 0[/tex]
[tex] {x}^{2} + 4x - 12 = 0[/tex]
[tex] {x}^{2} + 6x - 2x - 12 = 0[/tex]
[tex]x(x + 6) - 2(x + 6) = 0[/tex]
[tex](x + 6)(x - 2) = 0[/tex]
[tex]1)x + 6 = 0 = > x = - 6[/tex]
[tex]2)x - 2 = 0 = > x = 2[/tex]
[tex]g) {x}^{2} + 25 = 10x + 25[/tex]
[tex] {x}^{2} = 10x \: | \div x[/tex]
[tex]x = 10[/tex]
[tex]h) {x}^{2} + 25 = 10x + 1[/tex]
[tex] {x}^{2} - 10x + 25 - 1 = 0[/tex]
[tex] {x}^{2} - 10x + 24 = 0[/tex]
[tex] {x}^{2} - 6x - 4x + 24 = 0[/tex]
[tex]x(x - 6) - 4(x - 6) = 0[/tex]
[tex](x - 6)(x - 4) = 0[/tex]
[tex]1)x - 6 = 0 = > x = 6[/tex]
[tex]2)x - 4 = 0 = > x = 4[/tex]
[tex]i) {x}^{2} + 8x + 15 = 0[/tex]
[tex] {x}^{2} + 3x + 5x + 15 = 0[/tex]
[tex]x(x + 3) + 5(x + 3) = 0[/tex]
[tex](x + 3)(x + 5) = 0[/tex]
[tex]1)x + 3 = 0 = > x = - 3[/tex]
[tex]2)x + 5 = 0 = > x = - 5[/tex]
[tex]j) {x}^{4} = 81[/tex]
[tex] {x}^{4} = {3}^{4} [/tex]
[tex]x = 3[/tex]
[tex]k) {x}^{2} + 3x + 2 = 0[/tex]
[tex] {x}^{2} + 2x + x + 2 = 0[/tex]
[tex]x(x + 2) + x + 2 = 0[/tex]
[tex](x + 2)(x + 1) = 0[/tex]
[tex]1)x + 2 = 0 = > x = - 2[/tex]
[tex]2)x + 1 = 0 = > x = - 1[/tex]
[tex]l) {x}^{2} - 2x + 3 = 0[/tex]
[tex]nu \: are \: radacini \: reale[/tex]
[tex]4)a) {x}^{2} - 1 = 24[/tex]
[tex] {x}^{2} = 24 + 1[/tex]
[tex] {x}^{2} = 25[/tex]
[tex]x = \pm \sqrt{25} [/tex]
[tex]x = \pm5[/tex]
[tex]b)4 {x}^{2} + 4x + 1 = 9[/tex]
[tex]4 {x}^{2} + 4x - 8 = 0[/tex]
[tex]\Delta = 16 - 4 \times 4 \times ( - 8) = 16 + 128 = 144[/tex]
[tex]x_{1} = \frac{ - 4 + 12}{8} = 1[/tex]
[tex]x_{2} = \frac{ - 4 - 12}{8} = - 2[/tex]
[tex]c) {(5x - 1)}^{2} = 36[/tex]
[tex]5x - 1 = \pm \sqrt{36} [/tex]
[tex]5x - 1 = \pm6[/tex]
[tex]1)5x- 1 = 6 = > 5x = 7 = > x = \frac{7}{5} [/tex]
[tex]2)5x - 1 = - 6 = > 5x = - 5 = > x = - 1[/tex]
[tex]d) {(2x - 3)}^{2} = 4[/tex]
[tex]2x - 3 = \pm \sqrt{4} [/tex]
[tex]2x - 3 = \pm2[/tex]
[tex]1)2x - 3 = 2 = > 2x = 5 = > x = \frac{5}{2} [/tex]
[tex]2)2x - 3 = - 2 = > 2x = 1 = > x = \frac{1}{2} [/tex]
[tex]e) {(2 - 3x)}^{2} = - 4[/tex]
[tex]2 - 3x = \pm \sqrt{ - 4} = > ecuatia \: nu \: are \: radacini \: reale[/tex]
[tex]f)25 {x}^{2} = 4[/tex]
[tex] {x}^{2} = \frac{4}{25} [/tex]
[tex]x = \pm \sqrt{ \frac{4}{25} } [/tex]
[tex]x = \pm \frac{ \sqrt{4} }{ \sqrt{25} } [/tex]
[tex]x = \pm \frac{2}{5} [/tex]
[tex]g)3 {x}^{2} = 27[/tex]
[tex] {x}^{2} = \frac{27}{3} [/tex]
[tex] {x}^{2} = 9[/tex]
[tex]x = \pm \sqrt{9} [/tex]
[tex]x = \pm3[/tex]
[tex]h) {x}^{2} = 11 - 6 \sqrt{2} [/tex]
[tex]x = \pm \sqrt{11 - 6 \sqrt{2} } [/tex]
[tex]i) {x}^{2} + 7 = 0[/tex]
[tex] {x}^{2} = - 7[/tex]
[tex]x = \pm \sqrt{ - 7} = > ecuatia \: nu \: are \: radacini \: reale[/tex]
[tex]j) \frac{x}{3} = \frac{3}{16x} [/tex]
[tex]16 {x}^{2} = 9[/tex]
[tex] {x}^{2} = \frac{9}{16} [/tex]
[tex]x = \pm \sqrt{ \frac{9}{16} } [/tex]
[tex]x = \pm \frac{ \sqrt{9} }{ \sqrt{16} } [/tex]
[tex]x = \pm \frac{3}{4} [/tex]
[tex]k) \frac{9}{25x} = \frac{x}{49} [/tex]
[tex]25 {x}^{2} = 441[/tex]
[tex] {x}^{2} = \frac{441}{25} [/tex]
[tex]x = \pm \sqrt{ \frac{441}{25} } [/tex]
[tex]x = \pm \frac{ \sqrt{441} }{ \sqrt{25} } [/tex]
[tex]x = \pm \frac{21}{5} [/tex]
[tex]l) \frac{5}{ {x}^{2} } = \frac{64}{5} [/tex]
[tex]64 {x}^{2} = 25[/tex]
[tex] {x}^{2} = \frac{25}{64} [/tex]
[tex]x = \pm \sqrt{ \frac{25}{64} } [/tex]
[tex]x = \pm \frac{ \sqrt{25} }{ \sqrt{64} } [/tex]
[tex]x = \pm \frac{5}{8} [/tex]
