Task/2616256
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(x² - x +1)(3x² -10x +3) =20x²
x =0 не корень 1*3 ≠0
(x² +1 -x) (3(x²+1) -10x) =20x² ;
( (x²+1)/x -1)(3(x²+1)/x -10)=20;замена: t =(x² +1) / x ; t ∈ (-∞ ; -2] U [2;∞)
( t -1)*(3t -10) = 20 ;
3t² - 13t -10 =0 ; D =13² - 4*3*(-10)= 289 =17²
t₁ = (13 -17)/(2*3) = - 2/3 → посторонний
t₂ =(13+17)/6 =5 .
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(x² +1) / x = 5 ;
x² - 5x +1 =0 ;
x =(5 ±√21)/2 .
ответ : (5 ±√21)/2 .
* * * * * * * P.S. * * * * * * *
(x +1/x)/2 ≥ √(x*1/x) , если x >0 ⇔x +1/x ≥ 2
(-x -1/x) /2 ≥ √(-x*(-1/x) ) , если x< 0 ⇔ x +1/x ≤ -2