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maruhashuba
@maruhashuba
July 2022
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(3х+2)²(4х-3)²≤(5х-1)² допоможіть розв'язати, я в математиці не дуже шарю
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nafanya2014
Verified answer
A²·b²=(ab)²
(ab)²-c²=(ab-c)(ab+c)
((3х+2)·(4х-3))²-(5х-1)²≤0
(12x²+8x-9x-6)²-(5x-1)²≤0
(12x²-x-6-5x+1)(12x²-x-6+5x-1)≤0
(12x²-6x-5)(12x²+4x-7)≤0
12x²-6x-5=0
D=36+240=276
x₁=(6-√276)/24 x₂=(6+√276)/24
12x²+4x-7=0
D=16+336=352
x₃=(-4-√352)/24 x₄=(-4+√352)/24
____+_____[x₃]___-____[x₁]____+____[x₄]_____-____[x₂]____+____
О т в е т. [(-4-√352)/24;(6-√276)/24]U[(-4+√352)/24;(6+√276)/24]
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Answers & Comments
Verified answer
A²·b²=(ab)²(ab)²-c²=(ab-c)(ab+c)
((3х+2)·(4х-3))²-(5х-1)²≤0
(12x²+8x-9x-6)²-(5x-1)²≤0
(12x²-x-6-5x+1)(12x²-x-6+5x-1)≤0
(12x²-6x-5)(12x²+4x-7)≤0
12x²-6x-5=0
D=36+240=276
x₁=(6-√276)/24 x₂=(6+√276)/24
12x²+4x-7=0
D=16+336=352
x₃=(-4-√352)/24 x₄=(-4+√352)/24
____+_____[x₃]___-____[x₁]____+____[x₄]_____-____[x₂]____+____
О т в е т. [(-4-√352)/24;(6-√276)/24]U[(-4+√352)/24;(6+√276)/24]