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rezolvati in R ecuatiiile a (2x+1) (x+1) = (x-2) (2x+5)
b) (x-1) (x+1) = x la a doua +2(x-3)
c) (4x-3)ori x= (-2x+0,5) totul la a doua

Răspuns :

[tex]a)(2x + 1)(x + 1) = (x - 2)(2x + 5)[/tex]

[tex] 2 {x}^{2} + 2x + x + 1 = 2 {x}^{2} + 5x - 4x - 10[/tex]

[tex] {2x}^{2} + 3x + 1 - 2 {x}^{2} - 5x + 4x + 10 = 0[/tex]

[tex]2x + 11 = 0[/tex]

[tex]2x = - 11[/tex]

[tex]x = - \frac{11}{2} [/tex]

[tex]x = - 5.5[/tex]

[tex]b)(x - 1)(x + 1) = {x}^{2} + 2(x - 3)[/tex]

[tex] {x}^{2} - 1 = {x}^{2} + 2x - 6[/tex]

[tex] {x}^{2} - {x}^{2} - 2x = - 6 + 1[/tex]

[tex] - 2x = - 5 \: | \times ( - 1)[/tex]

[tex]2x = 5[/tex]

[tex]x = \frac{5}{2} [/tex]

[tex]x = 2.5[/tex]

[tex]c)(4x - 3) \times x = {( - 2x + 0.5)}^{2} [/tex]

[tex]4 {x}^{2} - 3x = 4 {x}^{2} - 2x + 0.25[/tex]

[tex]4 {x}^{2} - 3x - 4 {x}^{2} + 2x = 0.25[/tex]

[tex] - x = 0.25 \: | \times ( - 1)[/tex]

[tex]x = - 0.25[/tex]

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