x = 2y-2
3*y=x+8
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ĐKXĐ: \(x\ge0;y\ge1\).
Đặt \(\left\{{}\begin{matrix}\sqrt[4]{y^3-1}=a\ge0\\\sqrt{x}=b\ge0\end{matrix}\right.\).
HPT đã cho trở thành:
\(\left\{{}\begin{matrix}a+b=3\\a^4+b^4=81\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b=3\\\left(a+b\right)^4-2ab\left(2a^2+3ab+2b^2\right)=81\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b=3\\ab\left(2a^2+3ab+2b^2\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}a=3;b=0\\a=0;b=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9;y=1\\x=0;y=\sqrt[3]{82}\end{matrix}\right.\).
Áp dụng t/c dtsbn ta có:
\(\dfrac{x}{23}=\dfrac{y}{2}=\dfrac{x+2y}{23+2.2}=\dfrac{-27}{27}=-1\)
\(\dfrac{x}{23}=-1\Rightarrow x=-23\\ \dfrac{y}{2}=-1\Rightarrow y=-2\)
\(\dfrac{x}{23}=\dfrac{y}{2}\text{ và }x+2y=-27\)
\(\text{Áp dụng tính chất dãy tỉ số bằng nhau:}\)
\(\dfrac{x}{23}=\dfrac{y}{2}=\dfrac{x+2y}{23+2.2}=\dfrac{-27}{27}=-1\)
\(\Rightarrow x=23.\left(-1\right)=-23\)
\(y=\left(-1\right).2=-2\)
\(\frac{x-3}{8}=\frac{y}{30}=\frac{z+1}{27}=\frac{3x-9}{24}=\frac{2y}{60}=\frac{5z+5}{135}=\frac{3x-9-\left(5z+5\right)+2y}{24-135+60}=\frac{3x-5z+2y-14}{-51}\)
\(=\frac{23-14}{-51}=\frac{9}{-51}=\frac{3}{-17}\)
\(\Rightarrow\hept{\begin{cases}x-3=\frac{8.3}{-17}=-\frac{24}{17}\Rightarrow x=\frac{-24}{17}+3=\frac{27}{17}\\y=\frac{30.3}{-17}=-\frac{90}{17}\\z+1=\frac{27.3}{-17}=-\frac{81}{17}\Rightarrow z=-\frac{81}{17}-1=-\frac{98}{17}\end{cases}}\)
2)ĐK:\(\begin{cases}x\ge-1\\...\\y^2+8x\ge0\end{cases}\)
pt(1)\(\Leftrightarrow2\left[\sqrt{x^2+5x-y+2}-\left(x+2\right)\right]+\left(x+2-\sqrt{y^2+8x}\right)=0\)
\(\Leftrightarrow\left(x-y-2\right)\left(\frac{2}{\sqrt{x^2+5x-y+2}+x+2}+\frac{x+y-2}{x+2+\sqrt{y^2+8x}}\right)=0\)
\(\Rightarrow\)y=x-2
Thay vào pt(2) ta được:x-9=\(\sqrt{x+1}\)
\(\Leftrightarrow\begin{cases}x\ge9\\x^2-19x+80=0\end{cases}\Leftrightarrow x=\frac{19+\sqrt{41}}{2}}\)
\(\Rightarrow\)(x;y)=(\(\frac{19+\sqrt{41}}{2};\frac{15+\sqrt{41}}{2}\))(t/m)
a) => y+42+2y= -12-14+2y
y+2y-2y = -12-14-42
y= -68
b) => 15+y-5-5y= -12-5y
y-5y+5y= -12-15+5
y = -22
c) => 2y+5-8y+21= -3-5y-2
2y-8y+5y= -3-2-5-21
-y= -31=>y=31
d)=> -13+3y+23= -120+y
3y-y= -120+13-23
2y= -130=>y= -65
e) => -21+32+5y= 16+4y
5y-4y= 16+21-32
y= 5
bài 1
a)y-(-42-2y) = (-12) - 14 +2y
y +42 + 2y = -12 -14 +2y
3y + 42 = -26 +2y
y = -68
b)15-(-y+5)-5y=-(12+5y+2)
15+y-5-5y=-12-5y-2
10-4y=-14-5y
-4y+5y=-14-10=-24
c)2y-(-5+8y-21)=-3-(5y+2)
2y+5-8y+21=-3y-5y-2
-6y+26=-8y-2
-6y+8y=-2-26
2y=-28
y=-28/2=-14
Bài 2:
a: =6(15-5)=6*10=60
b: =9(-3+23)=9*20=180
c: =11(-10+210)=11*200=2200
d: =125*4+125*4=125*8=1000