`40/(x+3) - 32/(x-3) = 8/3`
`=> 120(x-3) - 96(x+3) = 8(x^2 - 9)`
`<=> 120x -360 -96x -288 =8x^2 - 72`
`<=> -8x^2 +24x -576=0`
`Δ=24^2 -4.(-8).(-576)=-17856`
vì` Δ <0`
`=>` pt vô nghiệm
GIẢI PHƯƠNG TRÌNH
a) \(\dfrac{1}{3}\sqrt{x-2}-\dfrac{2}{3}\sqrt{9x-18}+6\sqrt{\dfrac{x-2}{81}}=-4\)
b) \(\sqrt{9x^2+12x+4}=4x\)
c) \(\sqrt{9x-18}-\sqrt{4x-8}+3\sqrt{x-2}=40\)
d) \(\sqrt{5x-6}-3=0\)
Phân tích đa thức thành nhân tử
a. \(\dfrac{1}{2}\left(x^2+y^2\right)^2-2x^2y^2\)
b. \(27x^3-\dfrac{1}{8}y^3\)
c. \(\dfrac{1}{2}x^2+\dfrac{1}{4}x+\dfrac{1}{32}\)
Giải các pt sau:
\(\dfrac{5}{x^2-2x+2}-\dfrac{8}{x^2-2x+5}=3\)
\(\dfrac{x^2-4x+3}{2x}+\dfrac{x^2+12x+3}{x^2+3}=4\)
giải các hệ phương trình
a \(\dfrac{5}{x-1}+\dfrac{1}{y-1}=10\)
\(\dfrac{1}{x-1}-\dfrac{3}{y-1}=18\)
b \(\dfrac{5}{x+y-3}-\dfrac{2}{x-y+1}=8\)
\(\dfrac{3}{x+y-3}+\dfrac{1}{x-y+1}=\dfrac{3}{2}\)
c \(\sqrt{x-1}-3\sqrt{y+2}=2\)
\(2\sqrt{x-1}+5\sqrt{y+2}=15\)
d \(\dfrac{7}{\sqrt{x-7}}-\dfrac{4}{\sqrt{y+6}}=\dfrac{5}{3}\)
\(\dfrac{5}{\sqrt{x-7}}+\dfrac{3}{\sqrt{y+6}}=\dfrac{13}{6}\)
e \(7x^2+13y=-39\)
\(5x^2-11y=33\)
f \(2\left(x-1\right)^2-3y^3=7\)
\(5\left(x-1\right)^2+6y^3=4\)
giải hệ phương trình
\(\left\{{}\begin{matrix}\dfrac{x+y}{xy}=\dfrac{3}{8}\\\dfrac{y+x}{yz}=\dfrac{3}{4}\\\dfrac{x+z}{xz}=\dfrac{5}{6}\end{matrix}\right.\)
giải các phương trình sau:
a \(x^3+x^2+x=-\dfrac{1}{3}\)
b \(x^3+2x^2-4x=-\dfrac{8}{3}\)
Cho 0<x,y,z<\(\dfrac{\sqrt{3}}{2}\) thỏa mãn xy+yz+zx=\(\dfrac{3}{4}\)
Tìm Min Q=\(\dfrac{4x^2}{x\left(32-4x^2\right)}+\dfrac{4y^2}{y\left(32-4y^2\right)}+\dfrac{4z^2}{z\left(32-4z^2\right)}\)
\(\left(6\right)\dfrac{3\sqrt{x}}{5\sqrt{x}-1}\le-3\)
\(\left(7\right)\dfrac{8\sqrt{x}+8}{6\sqrt{x}+9}>\dfrac{8}{3}\)
\(\left(8\right)\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}< -4\)
\(\left(9\right)\dfrac{4\sqrt{x}+6}{5\sqrt{x}+7}\le-\dfrac{2}{3}\)
\(\left(10\right)\dfrac{6\sqrt{x}-2}{7\sqrt{x}-1}>-6\)
Giải phương trình :
a) \(\sqrt{2x^2-\sqrt{2}x+\dfrac{1}{4}}=\sqrt{2}x\)
b)\(\sqrt{4x+8}+\dfrac{1}{3}\sqrt{9x+18}=3\sqrt{\dfrac{x+2}{4}}+\sqrt{2}\)
40. B=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\right).\left(\dfrac{\sqrt{x}-2}{3}+1\right)\)
b. Rút gọn B
