Question

решите дча примера на листочке

Answer 1

Решить неравенства:

5. |x²-8x+15|≤|15-x²|

6. 3|x-2|+|5x-4|≤10

Решение:

$boxed 5 \ \ tt |x^2-8x+15|leq |15-x^2| \ (x^2-8x+15)^2 leq (15-x^2)^2 \ (x^2-8x+15)^2 - (15-x^2)^2 leq 0 \ (x^2-8x+15-15+x^2)(x^2-8x+15+15-x^2) leq 0 \ (2x^2-8x)(-8x+30) leq 0 \ x(x-4)(-4x+15) leq 0$

___+___[0]___-___[15/4]___+___[4]___-___

x∈[0; 15/4]U[4; +∞)

$boxed 6 \ \ tt 3|x-2|_{(1)}+|5x-4|_{(2)} leq 10 \ \ x-2=0 Rightarrow x=2 \ 5x-4=0 Rightarrow x=0,8 \ \ 1) x<0,8 (1-, 2-) \ \ -3x+6-5x+4 leq 10 \ -8x leq 0 \ x geq 0 \ \ x in [0; 0,8) \ \ 2) x in [0,8; 2) (1-, 2+) \ \ -3x+6+5x-4 leq 10 \ 2x leq8 \ x leq 4 \ \x in [0,8; 2) \ \ 3) x geq 2 (1+, 2+) \ \ 3x-6+5x-4 leq 10 \ 8x leq 20 \ x leq 2,5 \ \ x in [2; 2,5]$

x∈[0; 2,5]