Theo bài ra , ta có : 

77x² + 23x² + 77.46 

= 77x² + 2.23.77x + 23² ( bn sai đề mik sửa lại một chút nhé =)) ) 

= ( 77x + 23 )²

\(\left(x-1\right)\left(x+2\right)-x-2=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+2\right)-\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)=0\)

\(\rightarrow\orbr{\begin{cases}x+2=0\\x-2=0\end{cases}\leftrightarrow\orbr{\begin{cases}x=-2\\x=2\end{cases}}}\)

\(8-27x^3\)

\(=2^3-\left(3x\right)^3\)

\(=\left(2-3x\right)\left(4+6x+9x^2\right)\)

a) \(8-27x^3=\left(2-x\right)\left(4+6x+9x^2\right)\)

b) \(27+27x+9x^2+x^3=\left(3+x\right)^3\)

c) \(x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)

\(2x^2+3x-5=0\)

\(\Leftrightarrow2x^2-2x+5x-5=0\)

\(\Leftrightarrow2x\left(x-1\right)+5\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(2x+5\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\2x+5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=\frac{-5}{2}\end{cases}}}\)

Giải:

2x² + 3x - 5 = 0 

=> (2x² - 2) + (3x - 3) = 0 

=> (2x + 5)(x-1) = 0

\(\Rightarrow\orbr{\begin{cases}x=-2,5\\x=1\end{cases}}\)

a² + b² + c² + 3,5 = a + 2b + 3c

<=> (a² - a + 0,25) + (b² - 2b + 1) + (c² - 3c + 2,25) = 0

<=> (a - 0,5)² + (b - 1)² + (c - 1,5)² = 0

<=> (a; b; c) = (0,5; 1; 1,5)

(1-2x)(1+2x)

\(\left(x+1\right)^2-25=\left(x+26\right)\left(x-24\right)\)

\(1-2y+y^2=\left(y-1\right)^2\)

\(\left(x+1\right)^2-25\)

\(=x^2+2x+1-25\)

\(=x^2+2x-24\)

\(=x^2+6x-4x-24\)

\(=x\left(x+6\right)-4\left(x+6\right)\)

\(=\left(x-4\right)\left(x+6\right)\)

\(1-2y+y^2\)

\(=1-y-y+y^2\)

\(=\left(1-y\right)-y\left(1-y\right)\)

\(=\left(1-y\right)\left(1-y\right)\)

\(=\left(1-y\right)^2\)

C2

\(1-2y+y^2=\left(1-y\right)^2\)