a: Ta có: \(\left(x-3\right)^2-x\left(x+5\right)=9\)

\(\Leftrightarrow x^2-6x+9-x^2-5x=9\)

\(\Leftrightarrow x=0\)

b: Ta có: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)

\(\Leftrightarrow x^3+8-x^3-2x=15\)

\(\Leftrightarrow2x=-7\)

hay \(x=-\dfrac{7}{2}\)

a. 6x² - (2x + 5)(3x - 2) = 7

<=> 6x² - 6x² + 4x - 15x + 10 = 7

<=> -11x = -3

<=> \(x=\dfrac{3}{11}\)

b. (5 - x)(25 + 5x + x²) + x(x² - 7) = 25

<=> 125 - x³ + x³ - 7x = 25

<=> -7x = 25 - 125

<=> -7x = -100

<=> \(x=\dfrac{100}{7}\)

c. (7 - 2x)² + (3 + 2x)(3 - 2x) = 30

<=> 49 - 28x + 4x² + 9 - 4x² = 30

<=> 4x² - 4x² - 28x = 30 - 49 - 9

<=> -28x = -28

<=> x = 1

Cảm ơn bạn rất nhiều ạ:3 <3

e) Ta có: \(E=\left(3x+2\right)\left(3x-5\right)\left(x-1\right)\left(9x+10\right)+24x^2\)

\(=\left(9x^2-15x+6x-10\right)\left(9x^2+10x-9x-10\right)+24x^2\)

\(=\left(9x^2-10-9x\right)\left(9x^2-10+x\right)+24x^2\)

\(=\left(9x^2-10\right)^2-8x\left(9x^2-10\right)-9x^2+24x^2\)

\(=\left(9x^2-10\right)^2-8x\left(9x^2-10\right)+15x^2\)

\(=\left(9x^2-10\right)^2-3x\left(9x^2-10\right)-5x\left(9x^2-10\right)+15x^2\)

\(=\left(9x^2-10\right)\left(9x^2-3x-10\right)-5x\left(9x^2-10-3x\right)\)

\(=\left(9x^2-3x-10\right)\left(9x^2-5x-10\right)\)

\(\left(x+2\right)^2-9=0\)

\(\Rightarrow\left(x+2\right)^2=9\)

\(\Rightarrow\left[{}\begin{matrix}x+2=3\\x+2=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\)

Vậy...

\(x^2-y^2+10x-10y=\left(x-y\right)\left(x+y\right)+10\left(x-y\right)=\left(x-y\right)\left(x+y+10\right)\)

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

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

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

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

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

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

(a^2 +b^2).(x^2 +y^2) > hoặc = (ax+by)^2 
dấu " = " xảy ra khi a/x = b/y 
Vì a/x =b/y => ay=bx 
(a^2 +b^2).( x^2 +y^2)= a^2.x^2 +a^2.y^2 +b^2.x^2 + b^2.y^2 
= a^2.x^2 + b^2.x^2 +b^2.x^2 +b^2.y^2 
= (ax)^2 +2.b^2.x^2 + (by)^2 
= (ax)^2 +2.ax.by + (by)^2 ( tách b^2.x^2= b.x.b.x = a.y.b.x= ax.by) 
= (ax+by)^2 
=> đpcm +5*hjhjhkj