Question

Решите плиз) нужно очень!

Answer 1

Ответ:

1) 1/3

2) [1; 3]

3) -1, 6, 2, 3

4) нет решений

Объяснение:

1)

$|x-2|-2x-1=0\\|x-2|=2x+1\\\left \{ {{x-2=2x+1} \atop {x-2\geq 0}} \right. , \left \{ {{x-2=-2x-1} \atop {x-2\leq 0}} \right. \\\left \{ {{-x=3} \atop {x\geq 2}} \right. ,\left \{ {{3x=1} \atop {x\leq 2}} \right.$

1 система не решается, вторая - $x=\frac{1}{3}$

2)

$|x-1|+|x-3|=2\\\\\left \{ {{x-1+x-3=2} \atop {\left \{ {{x-1\geq 0} \atop {x-3\geq 0}} \right.}} \right. , \left \{ {{x-1-x+3=2} \atop {\left \{ {{x-1\geq 0} \atop {x-3\leq 0}} \right.}} \right. , \left \{ {{-x+1+x-3=2} \atop {\left \{ {{x-1\leq 0} \atop {x-3\geq 0}} \right.}} \right. ,\left \{ {{-x+1-x+3=2} \atop {\left \{ {{x-1\leq 0} \atop {x-3\leq 0}} \right.}} \right.$

$\left \{ {{2x=6} \atop {\left \{ {{x\geq 1} \atop {x\geq 3}} \right.}} \right. , \left \{ {{0x=0} \atop {\left \{ {{x\geq 1} \atop {x\leq 3}} \right.}} \right. , \left \{ {{0x=4} \atop {\left \{ {{x\leq 1} \atop {x\geq 3}} \right.}} \right. ,\left \{ {{-2x=-2} \atop {\left \{ {{x\leq 1} \atop {x\leq 3}} \right.}} \right.$

$\left \{ {{x=3} \atop {x\geq 3}} \right. , \left \{ {{0x=0} \atop {1\leq x\leq 3}} \right. , \left \{ {{0x=4} \atop {x\leq 1, x\geq 3}} \right. , \left \{ {{-2x=-2} \atop {x\leq 1}} \right.$

x=3, x ∈ [1; 3], x ∈ ∅, x ∈ ∅

x ∈ [1; 3]

3)

$|x^2-5x|=6\\\left \{ {{x^2-5x-6=0} \atop {x^2-5x\geq 0}} \right. , \left \{ {{x^2-5x+6=0} \atop {x^2-5x\leq 0}} \right. \\\left \{ {{\left \{ {{x=-1} \atop {x=6}} \right. } \atop {\left \{ {{x\leq 0} \atop {x\geq 5}} \right. }} \right. , \left \{ {{\left \{ {{x=2} \atop {x=3}} \right. } \atop {\left \{ {{x\geq 0} \atop {x\leq 5}} \right. }} \right.$

x = -1, x = 6, x = 2, x = 3

4)

$|x+3|<x-2\\\left \{ {{x+3-x+2<0} \atop {x+3\geq 0}} \right. , \left \{ {{-x-3-x+2<0} \atop {x+3\leq 0}} \right. \\\left \{ {{5<0} \atop {x\geq -3}} \right. , \left \{ {{-2x<1} \atop {x\leq -3}} \right.$

x ∈ ∅, x ∈ ∅