Решите неравенство (3х+2)^2+(4x-3)^2≤(5x-1)^2
Решение:
(9x^+12x+4)*2+(16x^-24x+9)*2<(25x^-10x+1)*2
(18x^+24x+8)+(32x^-48x+18)<(50x^-20x+2)
18x^+24x+8+32x^-48x+18<50x^-20x+2
50x^-24x+26<50x^-20x+2
50x^-24x+26-50x^+20x-2<0 50x^сокращается
-4x+24<0
-4x<0
x>6
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Решение:
(9x^+12x+4)*2+(16x^-24x+9)*2<(25x^-10x+1)*2
(18x^+24x+8)+(32x^-48x+18)<(50x^-20x+2)
18x^+24x+8+32x^-48x+18<50x^-20x+2
50x^-24x+26<50x^-20x+2
50x^-24x+26-50x^+20x-2<0 50x^сокращается
-4x+24<0
-4x<0
x>6