Решить систему уравнений) 1) 3-х>1 х²-9≤9 2) х²≥4 х-3<0 3) 6х-х²>0 3-2х>х

Question

Решить систему уравнений)
1)
3-х>1
х²-9≤9
2)
х²≥4
х-3<0<br> 3)
6х-х²>0
3-2х>х

Answer 1

1)
{3-x>1
{x²-9≤9

3-x>1
-x>1-3
-x>-2
x<2<br>
x²-9≤9
x²-9-9≤0
x²-18≤0
(x-√18)(x+√18)≤0
(x-3√2)(x+3√2)≤0
x=3√2      x=-3√2
     +                      -                       +
------- -3√2 ------------ 3√2 --------------
                   \\\\\\\\\\\\\\\\\\ 
-3√2 ≤ x ≤ 3√2

{x<2<br>{-3√2 ≤ x ≤ 3√2
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-------- -3√2 --------- 2 ---------- 3√2 --------------
                  \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
-3√2 ≤ x <2<br>x∈[-3√2; 2)

2.
{x² ≥4
{x-3<0<br>
x² ≥4
x²-4≥0
(x-2)(x+2)≥0
x=2       x=-2
           +                      -                   +
----------- -2 -------------- 2 -------------
\\\\\\\\\\\\\\                             \\\\\\\\\\\\\\\\\\\\\\
x≤-2
x≥2

x-3<0<br>x<3<br>
{x≤ -2
{x≥ 2
{x<3<br>\\\\\\\\\\\                        \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
------- -2 ------------- 2 ----- 3 ----------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(-∞; -2] U [2; 3)

3.
{6x-x²>0
{3-2x>x

6x-x²>0
x²-6x<0<br>x(x-6)<0<br>x=0    x=6
     +                 -                   +
--------- 0 ----------- 6 ------------
                \\\\\\\\\\\\\
0
3-2x>x
-2x-x> -3
-3x> -3
x<1<br>
{0{x<1<br>               \\\\\\\\\\\\\\\\\\\\\\\\\\\\
------- 0 ---------- 1 ------------ 6 ------------------
\\\\\\\\\\\\\\\\\\\\\\\\\\
0x∈(0; 1)