решите методом интервалов неравенства [tex] \frac{2 x^{2} -4x-6}{4x-11} \geq 2[/tex]. Created by NellRus1. algebra-ru

___________________________________________2x²-12x+16=0 (делим на 2)x²-6x+8=0 D=b²-4ac=36-4*1*8=36-32=4x1=x2=x²-6x+8=(x-4)(x-2)__________________________Нули функции: x=4, x=2, x=Ответ: []U[4;+∞) График смотри во вложении.

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NellRus1 @NellRus1

August 2021 1 10 Report

решите методом интервалов неравенства
[tex] \frac{2 x^{2} -4x-6}{4x-11} \geq 2[/tex]

Answers & Comments

MashaBaggins $\frac{2x^2-4x-6}{4x-11} \geq 2$
$\frac{2x^2-4x-6}{4x-11}-2 \geq 0$
$\frac{2x^2-4x-6-2(4x-11)}{4x-11} \geq 0$
$\frac{2x^2-4x-6-8x+22}{4x-11} \geq 0$
$\frac{2x^2-12x+16}{4x+11} \geq 0$
___________________________________________
2x²-12x+16=0 (делим на 2)
x²-6x+8=0
D=b²-4ac=36-4*1*8=36-32=4
x1= $\frac{-b+ \sqrt{D} }{2a}= \frac{6+2}{2}=4$
x2= $\frac{-b- \sqrt{D} }{2a}= \frac{6-2}{2}=2$
x²-6x+8=(x-4)(x-2)
__________________________
$\frac{(x-4)(x-2)}{(4x-11) } \geq 0$
Нули функции: x=4, x=2, x= $2 \frac{3}{4}$

Ответ: [ $2;2 \frac{3}{4})$ ]U[4;+∞)
График смотри во вложении.

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