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Ответ:

а) х₁ = -0,75, х₂ = 0,625.

б) х₁ = -1, х₂ = -0,125.

в) х₁ = -0,4, х₂ = 0,7.

г) х₁ = -0,625, х₂ = [tex]\frac{1}{3}[/tex].

Пошаговое объяснение:

[tex]\frac{8x^{2} +x}{8} =\frac{15}{32} \\ \\ 32(8x^{2} +x) = 120\\ \\ 4(8x^{2} +x)=15\\ \\ 4(8x^{2} +x)-15=0\\ \\ 32x^{2} +4x-15=0\\ \\ 32x^{2} +24x-20x-15=0\\ \\ 8x(4x+3)-5(4x+3)=0\\ \\ (4x+3)(8x-5)=0[/tex]

Тогда 4х₁ + 3 = 0       и      8х₂ - 5 = 0,

          4х₁ = 0 - 3 = -3         8х₂ = 0 + 5 = 5

          х₁ = -3 ÷ 4 = -0,75    х₂ = 5 ÷ 8 = 0,625.

[tex]\frac{2x^{2} -3x}{2} +\frac{9x+2}{3} =\frac{3 - 2x^{2} }{6} \\ \\ 3(2x^{2} -3x)+2(9x+2)=3 - 2x^{2} \\ \\ 6x^{2} -9x+18x+4=3-2x^{2} \\ \\ 6x^{2} +9x+4=3-2x^{2} \\ \\ 6x^{2} +9x+4-3+2x^{2} =0\\ \\ 8x^{2} +8x+x+1=0\\ \\ 8x(x+1)+1(x+1)=0\\ \\ (x+1)(8x+1)=0[/tex]

Тогда х₁ + 1 = 0   и     8х₂ + 1 = 0

          х₁ = 0 - 1 = -1     х₂ = (0 - 1) ÷ 8 = -1 ÷ 8 = -0,125.

[tex]\frac{10x^{2} -3x}{2} =\frac{7}{5} \\ \\ 5(10x^{2} -3x)=14\\ \\ 5(10x^{2} -3x)-14=0\\ \\ 50x^{2} -15x-14=0\\ \\ 50x^{2} +20x-35x-14=0\\ \\ 10x(5x+2)-7(5x+2)=0\\ \\ (5x+2)(10x-7)=0[/tex]

Тогда 5х₁ + 2 = 0       и     10х₂ - 7 = 0

           5х₁ = 0 - 2 = -2       10х₂ = 0 + 7 = 7

           х₁ = -2 ÷ 5 = -0,4     х₂ = 7 ÷ 10 = 0,7.

[tex]\frac{7x + 15}{12} -\frac{6x^{2}+1}{6} =\frac{3 - 6x^{2} }{2} \\ \\ 7x+15 - 2(6x^{2} +1) = 6(3 - 6x^{2} )\\ \\ 7x+15-12x^{2} -2=18-36x^{2} \\ \\ 7x+13-12x^{2} =18-36x^{2} \\ \\ 7x+13-12x^{2} -18+36x^{2} =0\\ \\ 7x-5+24x^{2} =0\\ \\ 24x^{2} +7x-5=0\\ \\ 24x^{2} +15x-8x-5=0\\ \\ 3x(8x+5)-1(8x+5)=0\\ \\ (8x+5)(3-1)=0[/tex]

Тогда 8х₁ + 5 = 0        и       3х₂ - 1 = 0

           8х₁ = 0 - 5 = -5          3х₂ = 0 + 1 = 1

           х₁ = -5 ÷ 8 = -0,625   х₂ = [tex]\frac{1}{3}[/tex].