290.
1)
(4x-3)²+(3x-7)² ≤ (5x+1)² +5x² +4x-123
16x² -24x+9+9x²-42x+49 ≤ 25x²+10x+1+5x²+4x-123
25x² -66x+58 ≤ 25x² +5x² +14x - 122
25x² - 25x² -5x² -66x -14x +58 + 122 ≤ 0
-5x² - 80x + 180 ≤ 0
x² +16x - 36 ≥ 0
x² + 16x -36=0
D=16² - 4*(-36)=256+144=400
x₁=(-16-20)/2= -18
x₂=(-16+20)/2=2
+ - +
-------- -18 ------------ 2 ------------
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x∈(-∞; -18]U[2; +∞)
2)
(5x-3)² + (12x+5)² ≤ (7-13x)² +34x² +17x+410
25x²-30x+9+144x²+120x+25 ≤ 49-182x+169x² +34x²+17x+410
169x²+90x+34 ≤ 169x² + 34x² - 165x+459
169x² - 169x² - 34x² +90x+165x+34-459 ≤ 0
-34x² +255x-425 ≤ 0
-2x² + 15x - 25 ≤ 0
2x² - 15x + 25 ≥ 0
2x² -15x + 25=0
D=15² - 4*2*25=225-200=25
x₁=(15-5)/4=2.5
x₂=(15+5)/4=5
+ - +
------- 2.5 ------------ 5 ------------
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x∈(-∞; 2.5]U[5; +∞)