Question

2≤x²+x<6 розвязати ............

Answer 1

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

Answer 2

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

x^2+x-6<0

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)

Answer 3

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

x^2+x-6<0

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)