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[tex]3(6 x^{2} -13 x+6) ^{2} - 10(6 x^{2} - 13x)=53[/tex]
[tex]3(6 x^{2} -13 x+6) ^{2} - 10(6 x^{2} - 13x)=53[/tex]
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Замена: 6x^2 - 13x = t3(t+6)^2 - 10t = 53
3t^2 + 36t + 108 - 10t - 53 = 0
3t^2 + 26t + 55 = 0
D = 16
t1 = -5, t2 = -11/3
1) 6x^2 - 13x + 5 = 0
D=49
x1=1/2= 0.5
x2=5/3
2) 6x^2 - 13x + 11/3 = 0
18x^2 - 39x + 11 = 0
D=729=27^2
x3=1/3
x4 = 11/6
Ответ: 11/6, 1/3, 1/2, 5/3