(x - y)^2 + (y - z)^2 + (z - x)^2 = 4(x^2 + y^2 + z^2 - xy - yz - zx)

<=> x^2 - 2xy + y^2 + y^2 - 2yz + z^2 + z^2 - 2zx + x^2 =  4(x^2 + y^2 + z^2 - xy - yz - zx)

<=> 2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2xz =  4(x^2 + y^2 + z^2 - xy - yz - zx)

<=> 2(x^2 + y^2 + z^2 - xy - yz - zx) = 4(x^2 + y^2 + z^2 - xy - yz - zx)

<=>  2(x^2 + y^2 + z^2 - xy - yz - zx) = 0

<=> 2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2xz = 0

<=> (x^2 - 2xy + y^2) + (y^2 - 2yz + z^2) + (z^2 - 2zx + x^2) = 0

<=> (x - y)^2 + (y - z)^2 + (z - x)^2 = 0

<=> x - y = 0 và y - z = 0 và z - x = 0

<=> x = y và y = z và z = x

<=> x = y = z

a. ĐKXĐ: x \(\ne\pm3\)

b. M = \(\frac{3}{x-3}+\frac{6x}{x^2-9}+\frac{x}{x+3}\)

= \(\frac{3\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{6x}{\left(x-3\right)\left(x+3\right)}+\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

= \(\frac{3x+9+6x+x^2-3x}{\left(x-3\right)\left(x+3\right)}\) = \(\frac{9+6x+x^2}{\left(x-3\right)\left(x+3\right)}\)= \(\frac{\left(x+3\right)^2}{\left(x-3\right)\left(x+3\right)}=\frac{x+3}{x-3}\)

c. M = 0 hay \(\frac{x+3}{x-3}=0\) => x + 3 = 0 <=> x = -3 (Loại)

a) ĐK : x khác ²/₃ ; x khác 0

\(\frac{x+5}{3x-2}=\frac{A}{x\left(3x-2\right)}\)

\(\Leftrightarrow\frac{x\left(x+5\right)}{x\left(3x-2\right)}=\frac{A}{x\left(3x-2\right)}\)

\(\Leftrightarrow A=x^2+5x\)

b) \(\frac{5x+10}{4x-8}\cdot\frac{4-2x}{x+2}\)

\(=\frac{5\left(x+2\right)}{4\left(x-2\right)}\cdot\frac{2\left(2-x\right)}{\left(x+2\right)}\)

\(=\frac{-5}{2}\)

tham khảo nek:

https://h.vn/hoi-dap/question/210735.html

# mui #

Chiều dài mpn lak 3m . Lực td lak 250 N lak lực nào m ???

−4x>−2x−5

Giá trị nào sau đây là nghiệm của bất phương trình −4x>−2x−5−4x>−2x−5

A. x=3

B. x=4

C. x=72x

D. x=2

ĐA : D

Ta có \(9\cdot\cdot\cdot564.6=1092877\cdot\)

mà \(6.4=24\)

\(\Rightarrow\)\(\cdot=4\)

\(\frac{1}{x-1}+\frac{1}{x-2}=\frac{1}{x+1}+\frac{1}{x+2}\)

\(=\frac{1}{x-1}+1+\frac{1}{x-2}+2-\frac{1}{x+1}-1-\frac{1}{x+2}-2=0\)

\(\Rightarrow\frac{x-1+1}{x-1}+\frac{x-2+2}{x-2}-\frac{x+1-1}{x+1}-\frac{x+2-2}{x+2}=0\)

\(\Rightarrow\frac{x}{x-1}+\frac{x}{x-2}-\frac{x}{x+1}-\frac{x}{x+2}=0\)

\(\Rightarrow x\left(\frac{1}{x-1}+\frac{1}{x-2}-\frac{1}{x+1}-\frac{1}{x+2}\right)=0\)

Vì \(\frac{1}{x-1}+\frac{1}{x-2}-\frac{1}{x+1}-\frac{1}{x+2}\ne0\)\(\Rightarrow x=0\)

áp dụng định lý pitago vào tam giac AEC

\(EC=\sqrt{AC^2+AE^2}\)

\(=\sqrt{8^2+6^2}\)

\(=10\)

Vậy \(EC=10\)

còn EH bạn?