a.

\(\left(x^2+x\right)^2-6x^2-6x+8=0\)

\(\Leftrightarrow\left(x^2+x\right)^2-6\left(x^2+x\right)+8=0\)

\(\Leftrightarrow\left(x^2+x\right)^2-2\left(x^2+x\right)-4\left(x^2+x\right)+8=0\)

\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)-4\left(x^2+x-2\right)=0\)

\(\Leftrightarrow\left(x^2+x-2\right)\left(x^2+x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+x-2=0\\x^2+x-4=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\\x=\dfrac{-1\pm\sqrt{17}}{2}\end{matrix}\right.\)

b.

\(\left(x^2+10x+16\right)\left(x^2+10x+24\right)-20=0\)

\(\Leftrightarrow\left(x^2+10x+16\right)\left(x^2+10x+16+8\right)-20=0\)

\(\Leftrightarrow\left(x^2+10x+16\right)^2+8\left(x^2+10x+16\right)-20=0\)

\(\Leftrightarrow\left(x^2+10x+16\right)^2-2\left(x^2+10x+16\right)+10\left(x^2+10x+16\right)-20=0\)

\(\Leftrightarrow\left(x^2+10x+16\right)\left(x^2+10x+14\right)+10\left(x^2+10x+14\right)=0\)

\(\Leftrightarrow\left(x^2+10x+14\right)\left(x^2+10x+26\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+10x+14=0\\x^2+10x+26=0\left(vn\right)\end{matrix}\right.\)

\(\Leftrightarrow x=-5\pm\sqrt{11}\)

\(\Leftrightarrow x^4+2x^3+2x^2-2x^2-4x-4=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2=0\\x^2+2x+2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2=2\\\left(x+1\right)^2+1=0\left(\text{vô nghiệm}\right)\end{matrix}\right.\) 

\(\Leftrightarrow x=\pm\sqrt{2}\)

a b c là dấu cộng ph k bạn?

1/a 1/b nữa là dấu gì vậy bạn?

\(7x^2-x+1=7\left(x^2-\dfrac{x}{7}+\dfrac{1}{196}\right)+\dfrac{27}{28}\)

\(=7\left(x-\dfrac{1}{14}\right)^2+\dfrac{27}{28}\ge\dfrac{27}{28}\forall x\)

\(Min=\dfrac{27}{28}\Leftrightarrow x=\dfrac{1}{14}\)

A=   7x² - x + 1 

A=  7( x² - 2.1/14x + 1/196) + 27/28 

A= 7(x - 1/14)² + 27/28

A = 7(x - 1/14)² ≥ 0  ⇔ 7(x-1/14)² +27/28 ≥ 27/28 

A(min)= 27/28 ⇔ x = 1/14

\(=2x^2\left(2x+1\right)+2x\left(2x+1\right)+\left(2x+1\right)\)

\(=\left(2x^2+2x+1\right)\left(2x+1\right)\)

Ta có :

4x³+6x²+4x+1

= (4x³+2x²)+(4x²+2x)+(2x+1)

= 2x²(2x+1)+2x(2x+1)+(2x+1)

= (2x²+2x+1)(2x+1)

a) \(A=\left(37^3+12^3\right):49-37\times12\)

\(=\left(37+12\right)\left(37^2+12^2-37\times12\right):49-37\times12\)

\(=37^2+12^2-2\times37\times12\)

\(=\left(37-12\right)^2=25^2=625\)

b) \(B=\left(52^3-48^3\right):4+52\times48\)

\(=\left(52-48\right)\left(52^2+48^2+52\times48\right):4+52\times48\)

\(=52^2+48^2+2\times52\times48\)

\(=\left(52+48\right)^2=100^2=10000\)