Question

Giải PT:

a, 3(1-2x)《 4(5-3x/2)

b, 4-(x-3)² - (2x-1)² > 12x

c, 2x-1/x-1

Answer 1

Đây là giải bất phương trình nhé bạn

a) Ta có: \(3\left(1-2x\right)< 4\left(5-\frac{3x}{2}\right)\)

\(\Leftrightarrow3-6x< 20-6x\)

\(\Leftrightarrow3-6x-20+6x< 0\)

hay -17<0(vô lý)

Vậy: \(S=\varnothing\)

b) Ta có: \(4-\left(x-3\right)^2-\left(2x-1\right)^2>12x\)

\(\Leftrightarrow4-\left(x^2-6x+9\right)-\left(4x^2-4x+1\right)-12x>0\)

\(\Leftrightarrow4-x^2+6x-9-4x^2+4x-1-12x>0\)

\(\Leftrightarrow-5x^2-2x-6>0\)

\(\Leftrightarrow-5\left(x^2+\frac{2}{5}x+\frac{6}{5}\right)>0\)

\(\Leftrightarrow x^2+\frac{2}{5}x+\frac{6}{5}< 0\)

\(\Leftrightarrow x^2+2\cdot x\cdot\frac{2}{10}+\frac{4}{100}+\frac{29}{25}< 0\)

\(\Leftrightarrow\left(x+\frac{1}{5}\right)^2+\frac{29}{25}< 0\)(vô lý)

Vậy: \(S=\varnothing\)