0;\\\frac{-180t^2+66t-6}{36t^2-11t-5}\geq 0;" alt="\frac{11*3^{x-1}-31}{4*3^{2x}-11*3^{x-1}-5}-5\geq 0;\\\frac{11*3^{x-1}-31-5(4*3^{2x}-11*3^{x-1}-5)}{4*3^{2x}-11*3^{x-1}-5}\geq 0;\\\frac{11*3^{x-1}-31-180*3^{2x-2}+55*3^{x-1}+25}{36*3^{2x-2}-11*3^{x-1}-5}\geq 0;\\t=3^{x-1}; t>0;\\\frac{-180t^2+66t-6}{36t^2-11t-5}\geq 0;" align="absmiddle" class="latex-formula">
-180t^2+66t-6=0;
-30t^2+11t-1=0;
D=121-4*30=1;
t=(-11+1)/-60=1/6;
t=(-11-1)/-60=1/5;
___________
36*t^2-11t-5=0;
D=121+4*5*36=841=29²;
t=(11+29)/36=10/9;
t=(11-29)/36=-4/9;∅, т.к. t>0;
+ - + -
___1/6___1/5___10/9___
t ∈ (0;1/6] ∪ [1/5;10/9);
x ∈ (-∞;log₃0,5] ∪ [log₃0,6;log₃10/3);
____________
7)0;\\\frac{8t-2t^2-8}{2t^2-32}\leq 0;" alt="\frac{8*8^x-40}{2*8^{2x}-32}-1\leq 0;\ \frac{8*8^x-40-2*8^{2x}+32}{2*8^{2x}-32}\leq 0;\\\frac{8*8^x-2*8^{2x}-8}{2*8^{2x}-32}\leq 0;\ t=8^x;\ t>0;\\\frac{8t-2t^2-8}{2t^2-32}\leq 0;" align="absmiddle" class="latex-formula">
-2t²+8t-8=0;
D=64-4*2*8=0;
t=-8/-4=2;
_________
2t²-32=0;
t²=16;
t=-4;∅, т.к. t>0;
t=4;
- + -
___2___4___
t ∈ (0;2] ∪ (4;∞);
x ∈ (-∞;1/3] ∪ (2/3;∞);
8)0;\\\frac{(t-5)(t^3-t^2-4)+4t^2-20}{t-5}\leq 0;\\\frac{t^4-t^3-4t-5t^3+5t^2+20+4t^2-20}{t-5}\leq 0;\\\frac{t^4-6t^3+9t^2-4t}{t-5}\leq 0;" alt="5^{3x}-5^{2x}+\frac{4*5^{2x}-20}{5^x-5}-4\leq 0;\\\frac{(5^x-5)(5^{3x}-5^{2x}-4)+4*5^{2x}-20}{5^x-5}\leq 0;\ t=5^x;\ t>0;\\\frac{(t-5)(t^3-t^2-4)+4t^2-20}{t-5}\leq 0;\\\frac{t^4-t^3-4t-5t^3+5t^2+20+4t^2-20}{t-5}\leq 0;\\\frac{t^4-6t^3+9t^2-4t}{t-5}\leq 0;" align="absmiddle" class="latex-formula">
t-5=0; t₁=5;
t⁴-6t³+9t²-4t=0;
t₂=0;
t³-6t²+9t-4=0;
(t³-4t²)-(2t²-8t)+(t-4)=0;
t²(t-4)-2t(t-4)+(t-4)=0;
(t-4)(t²-2t+1)=0;
t₃=4;
t²-2t+1=0;
(t-1)²=0;
t₄=1;
- + ! + - +
__0___1___4___5___
t ∈ [1] ∪ [4;5);
x ∈ [0] ∪ [log₅4;1);