4x(4x^2-10x+7)+3x(4x^2-8x+7)=(4x^2-8x+7)(4x^2-10x+7)
16x^3-40x^2+28x+12x^3-24x^2+21x=16x^4-40x^3+28x^2-32x^3+80x^2-56x+28x^2-70x+49
28x^3-64x^2+49x=16x^4-72x^3+136x^2-126x+49
100x^3-200x^2+175x-49-16x^4=0
-16x^4+100x^3-200x^2+175x-49=0/-1
16x^4-100x^3+200x^2-175x+49=0
(2x-7)(2x-1)(4x^2-9x+7)=0
1)2x-7=0
2x=7
x=7/2
2)2x-1=0
2x=1
x=1/2
3)4x^2-9x+7=0
d=81-112=-31<0
Ответ:( 7/2:1/2)
Сумма корней: 7/2+1/2=8/2=4
3c(4x⁵-12c³)= 3с·4х⁵- 3с·12с³=12сх⁵-36с⁴
1/(3 - lgx) + 2/(lgx - 1) = 3;
(lgx - 1 + 6 - 2lgx)/((3 - lgx)(lgx - 1)) = 3;
-lgx + 5 = 3(3 - lgx) (lgx - 1);
-lgx + 5 = 9lgx - 9 - 3lg^2x + 3lgx;
-3lg^2x + 13lgx - 14 = 0;
lgx = a;
-3a^2 + 13a - 14 = 0;
D = 169 - 168 = 1;
a = - 2, a = 14/6 = 7/3;
lgx = -2 => 10^-2 = x, x = 1/100 = 0,01;
lgx = 7/3 => x = 10^(7/3).
Ответ: 0,01; 10^(7/3).