Đề:

Giá trị của y thoả mãn x² + y² + z² = xy + 3y + 2z - 4 với x, y, z \(\in\) Z.

Giải:

x² + y² + z² = xy + 3y + 2z - 4

x² - xy + y² - 3y + z² - 2z + 4 = 0

\(x^2-2\times x\times\frac{y}{2}+\frac{y^2}{4}+\frac{3y^2}{4}-3y+3+z^2-2z+1=0\)

\(\left(x-\frac{y}{2}\right)^2+3\left(\frac{y^2}{4}-2\times\frac{y}{2}\times1+1^2\right)+\left(z-1\right)^2=0\)

\(\left(x-\frac{y}{2}\right)+3\left(\frac{y}{2}-1\right)^2+\left(z-1\right)^2=0\)

\(\left\{\begin{matrix}x-\frac{y}{2}=0\\\frac{y}{2}-1=0\\z-1=0\end{matrix}\right.\)

\(\frac{y}{2}=1\)

\(y=2\)

ĐS: 2

~ Nana ~

Câu 1: Tính:

a) (2x⁴ - 3x³ - 3x² + 6x - 2) : (x² - 2)

b) \(\frac{4}{x+2}\)+ \(\frac{3}{x-2}\)+ \(\frac{5x+2}{4-x^2}\)

c) \(\frac{1-2x}{2x}\)+ \(\frac{2x}{2x-1}\)+ \(\frac{1}{2x-4x^2}\)

d) \(\frac{1}{a\left(a-b\right)\left(a-c\right)}\)+ \(\frac{1}{b\left(b-a\right)\left(b-c\right)}\)+ \(\frac{1}{c\left(c-a\right)\left(c-b\right)}\)

e) \(\frac{x-y}{xy}\)+\(\frac{y-z}{yz}\)+ \(\frac{z-x}{zx}\)

f) x² + 1 - \(\frac{x^4-3x^2+2}{x^2-1}\)

a.\(\frac{1}{x}\)+\(\frac{1}{y}\)+\(\frac{1}{2xy}\)=\(\frac{1}{2}\)(x,y\(\varepsilon\)N)

b.\(\frac{1}{x^2\left(x^2+y^2\right)}\)+\(\frac{1}{\left(x^2+y^2\right)\left(x^2+y^2+z^2\right)}\)+\(\frac{1}{\left(x^2+y^2+z^2\right)x^2}\)=1

c.2x⁶+y²-2x³y=320

Giai pt nghiem nguyen

thực hiện phép tính

a) (x³+8y³):(2y+x) b.\(\frac{a-1}{2\left(a-4\right)}+\frac{a}{a-4}\) c. (x³+3x²y+3xy²+y³):(2x+2y)

d. (x-5)²+(7-x)(x+2) e.\(\frac{3x}{x-2}-\frac{2x+1}{2-x}\) f. \(\left(\frac{x+2}{x+1}-\frac{2x}{x-1}\right)\cdot\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)

g.\(\left(\frac{1}{x+1}-\frac{3}{x^{3^{ }}+1}+\frac{3}{x^2-x+1}\right)\cdot\left(\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}\right)\) h.\(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x+6}{4-9x^2}\)

Nguyễn Nam giúp giùm

thực hiện pháp tính sau:

a) (x³+8y³):(2y+x)       b.\(\frac{a-1}{2\left(a-4\right)}+\frac{a}{a-4}\)  c. (x³+3x²y+3xy²+y³):(2x+2y)

d. (x-5)²+(7-x)(x+2)          e.\(\frac{3x}{x-2}-\frac{2x+1}{2-x}\)          f. \(\left(\frac{x+2}{x+1}-\frac{2x}{x-1}\right)\cdot\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)

g.\(\left(\frac{1}{x+1}-\frac{3}{x^{3^{ }}+1}+\frac{3}{x^2-x+1}\right)\cdot\left(\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}\right)\) h.\(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x+6}{4-9x^2}\)

Bài 1: thực hiện phép tính

a, \(\frac{\left(-x^{10}\right)}{-x^4}\)

b, \(\frac{\left(-x\right)^5.\left(-y\right)^4}{\left(x^2y\right)^2}\)

c, \(\frac{\frac{-2}{5}x^6y^3}{\frac{1}{5}.\left(-x\right)^3y^2}\)

d, \(\frac{2}{3}\)x²(-y)⁵:(2x²y)³

e, \(\frac{20^{10}}{10^3.6^5}\)

1/Thực hiện phép tính :

a)\(\left(\frac{1}{2}a^2x^4+\frac{4}{3}ax^3-\frac{2}{3}ax^2\right)\): \(\left(-\frac{2}{3}ax^2\right)\)

b) \(4\left(\frac{3}{4}x-1\right)+\left(12x^2-3x\right):\left(-3x\right)-\left(2x+1\right)\)

2/Rút gọn biểu thức:

((x³+y³)-2(x²-y²)+3(x+y)²) : (x+y)

3/Chia các đa thức:

a)(3x⁴-2x³-2x²+4x-8):(x²-2)

b)(2x³-26x-24):(x²+4x+3)

c)(x³-7x+6):(x+3)