2≤x²+x<6 розвязати ............

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2≤x²+x<6 розвязати ............

Алгебра (4.9k баллов) | 39 просмотров
Дано ответов: 3
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Правильный ответ

Решите задачу:

2\leq x^2+x<6\quad \Rightarrow \; \; \left \{ {{x^2+x\geq 2} \atop {x^2+x<6}} \right.\; \left \{ {{x^2+x-2\geq 0} \atop {x^2+x-6<0}} \right. \; \left \{ {{(x-1)(x+2)\geq 0} \atop {(x-2)(x+3)<0}} \right. \\\\\left \{ {{x\in (-\infty ,-2\, ]\cup [\, 1,+\infty )} \atop {x\in (-3,2)}} \right.\; \; \Rightarrow \; \; \; x\in (-3,-2\, ]\cup [\, 1,2)\\\\\\+++++++[\, -2\, ]----[\, 1\, ]++++++\\+++(-3)-----------(2)+++

(829k баллов)
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x^2+x≥2

x^2+x-2≥0

D=1+8=9

x1=(-1+3)/2*1=2/2=1

x2=(-1-3)/2*1=-4/2=-2


(-oo;-2]U[1;+oo)


x^2+x<6</p>

x^2+x-6<0</p>

D=1+24=25

x1=(-1+5)/2*1=4/2=2

x2=(-1-5)/2*1=-6/2=-3

(-3;2)

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______-3_____________-2__________1_________2_________

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(-3;-2]U[1;2)


(41.4k баллов)
0 голосов

x^2+x≥2

x^2+x-2≥0

D=1+8=9

x1=(-1+3)/2*1=2/2=1

x2=(-1-3)/2*1=-4/2=-2


(-oo;-2]U[1;+oo)


x^2+x<6</p>

x^2+x-6<0</p>

D=1+24=25

x1=(-1+5)/2*1=4/2=2

x2=(-1-5)/2*1=-6/2=-3

(-3;2)

///////////////////////////////////////////////////////////////////

______-3_____________-2__________1_________2_________

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\


(-3;-2]U[1;2)


(41.4k баллов)
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