77. Tìm x biết
a) \((x-1)^3 + (2-x)(4+2x+x^2) + 3x(x+2) = 17\)
b) \((x+2)(x^2 - 2x + 4) - x(x^2 - 2) = 15\)
c) \((x-3)^3 - (x-3)(x^2 + 3x + 9) + 9(x+1)^2 = 15\)
d) \(x(x-5)(x+5) - (x+2)(2)(x^2 - 2x + 4) = 3\)
78. Tìm x, y biết
a) \(\frac{1}{(x-1)^2} + (y+2x)^2 = 0\)
b) \(\frac{1}{(2x-1)^2} + (x-y)^2 = 0\)
c) \(x^2 + y^2 - 2x + 4y + 5 = 0\)
d) \(5x^2 + 2y^2 - 2x - 4y - 4xy + 5 = 0\)
e) \(x^2 + y^2 + 2x - 6y + 10 = 0\)
77:
a: \(\left(x-1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)=17\)
=>\(x^3-3x^2+3x-1+8-x^3+3x^2+6x=17\)
=>9x+7=17
=>9x=10
=>\(x=\frac{10}{9}\)
b: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-2\right)=15\)
=>\(x^3+8-x^3+2x=15\)
=>2x+8=15
=>2x=15-8=7
=>\(x=\frac72\)
c: \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+9\left(x+1\right)^2=15\)
=>\(x^3-9x^2+27x-27-\left(x^3-27\right)+9\left(x^2+2x+1\right)=15\)
=>\(-9x^2+27x+9x^2+18x+9=15\)
=>45x=15-9=6
=>\(x=\frac{6}{45}=\frac{2}{15}\)
d: \(x\left(x-5\right)\left(x+5\right)-\left(x+2\right)\left(x^2-2x+4\right)=3\)
=>\(x\left(x^2-25\right)-\left(x^3+8\right)=3\)
=>\(x^3-25x-x^3-8=3\)
=>-25x=8+3=11
=>\(x=-\frac{11}{25}\)
78:
a: \(\left(x-1\right)^2+\left(y+2x\right)^2=0\)
=>\(\begin{cases}x-1=0\\ y+2x=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=-2x=-2\end{cases}\)
b: \(\left(2x-1\right)^2+\left(x-y\right)^2=0\)
=>\(\begin{cases}2x-1=0\\ x-y=0\end{cases}\Rightarrow\begin{cases}x=\frac12\\ y=x=\frac12\end{cases}\)
c: \(x^2+y^2-2x+4y+5=0\)
=>\(x^2-2x+1+y^2+4y+4=0\)
=>\(\left(x-1\right)^2+\left(y+2\right)^2=0\)
=>\(\begin{cases}x-1=0\\ y+2=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=-2\end{cases}\)
d: \(5x^2+2y^2-2x-4y-4xy+5=0\)
=>\(x^2-2x+1+4x^2-4xy+y^2+y^2-4y+4=0\)
=>\(\left(x-1\right)^2+\left(y-2\right)^2+\left(2x-y\right)^2=0\)
=>\(\begin{cases}x-1=0\\ y-2=0\\ 2x-y=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=2\end{cases}\)
e: \(x^2+y^2+2x-6y+10=0\)
=>\(x^2+2x+1+y^2-6y+9=0\)
=>\(\left(x+1\right)^2+\left(y-3\right)^2=0\)
=>\(\begin{cases}x+1=0\\ y-3=0\end{cases}\Rightarrow\begin{cases}x=-1\\ y=3\end{cases}\)
