\(14^2=\left(a+2b+3c\right)^2\)

\(\left(a+2b+3c\right)^2\le\left(1+4+9\right)\left(a^2+b^2+c^2\right)\)

\(\rightarrow a^2+b^2+c^2\ge14\left(đpcm\right)\)

\(678-545=133\)

Số tự nhiên có 2 chữ số là: \(10,11,12,...,97,98,99\)

 Số tự nhiên có 2 chữ số là:

\(\left(99-10\right):1+1=90\) (số hạng)

Tổng của số tự nhiên có 2 chữ số là:

\(\left(99+10\right)\cdot90:2=4905\)

\(1,x^3-3x^2+3x-1=x^3-3\cdot x^2\cdot1+3\cdot x\cdot1^2-1^3=\left(x-1\right)^3\\ 2,x^3+3x^2+3x+1=x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3=\left(x+1\right)^3\\ 3,8x^3+12x^2+6x+1=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3=\left(2x+1\right)^3\\ 4,8x^3-12x^2+6x-1=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1-1^3=\left(2x-1\right)^3\\ 5,8-36x+54x^2-27x^3=2^3-3\cdot2^2\cdot3x+3\cdot2\cdot\left(3x\right)^2-\left(3x\right)^3=\left(2-3x\right)^3\\ 6,8+36x+54x^2+27x^3=2^3+3\cdot2^2\cdot3x+3\cdot2\cdot\left(3x\right)^2+\left(3x\right)^3=\left(2+3x\right)^3\\ 7,8x^3-12x^2y+6xy^2-y^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3=\left(2x-y\right)^3\\ 8,8x^3+12x^2y+6xy^2+y^3=\left(2x\right)^3+3\cdot2x\cdot y+3\cdot2x\cdot y^2+y^3=\left(2x+y\right)^3\)

\(15,4x^2-12x+9=\left(2x\right)^2-2\cdot2x\cdot3+3^2=\left(2x-3\right)^2\\ 18,9x^2-24xy+16y^2=\left(3x\right)^2-2\cdot3x\cdot4y+\left(4y\right)^2=\left(3x-4y\right)^2\\ 19,\dfrac{x^2}{4}+2xy+4y^2=\left(\dfrac{x}{2}\right)^2+2\cdot\dfrac{x}{2}\cdot2y+\left(2y\right)^2=\left(\dfrac{x}{2}+2y\right)^2\\ 20,-x^2+10x-25=-\left(x^2-10x+25\right)=-\left(x^2-2\cdot x\cdot5+5^2\right)=-\left(x-5\right)^2\)

\(15,4x^2-12x+9 =\left(2x\right)^2-2\cdot2x\cdot3+3^3 =\left(2x-3\right)^3\\ 16,4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\\ 17,1+12x+36x^2=1^2+2\cdot1\cdot6x+\left(6x\right)^2=\left(1+6x\right)^2\)

\(220-\left[3^2\cdot3^3-\left(12-7^0\right)^2\right]\\ =220-\left[3^5-11^2\right]\\ =220-\left[243-121\right]\\ =220-122\\ =98\)

\(a,126=1\cdot10^2+2\cdot10+6\cdot10^0\\ b,1068=1\cdot10^3+0\cdot10^2+6\cdot10^1+8\cdot10^0\\ c,a0b=a\cdot10^2+0\cdot10^1+b\cdot10^0\\ d,a0bc=a\cdot10^3+0\cdot10^2+b\cdot10^1+c\cdot10^0\)

\(a,\left(2x-1\right)^3=27\\ \Rightarrow\left(2x-1\right)^3=3^3\\ \Rightarrow2x-1=3\\ \Rightarrow2x=4\\ \Rightarrow x=2\\ b,\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=4\\ \Rightarrow x=2\\ c,\left(x+2\right)^3=\left(2x\right)^3\\ \Rightarrow x+2=2x\\ \Rightarrow2x-x=2\\ \Rightarrow x=2\\ d,\left(2x-1\right)^7=x^7\\ \Rightarrow2x-1=x\\ \Rightarrow2x-x=1\\ \Rightarrow x=1\)

\(a,x^2=16\\ \Rightarrow x^2=\left(\pm4\right)^2\\ \Rightarrow x=\pm4\)

\(b,x^3=27\\ \Rightarrow x^3=3^3\\ \Rightarrow x=3\)

\(c,2\cdot x^3-4=12\\ \Rightarrow2\cdot x^3=16\\ \Rightarrow x^3=16:2\\ \Rightarrow x^3=8\\ \Rightarrow x^3=2^3\\ \Rightarrow x=2\)

\(d,5x^3-5=0\\ \Rightarrow5\left(x^3-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}5=0\left(l\right)\\x^3-1=0\end{matrix}\right.\\ \Rightarrow x^3=1\\ \Rightarrow x=1\)

\(e,\left(x+1\right)^2=16\\ \Rightarrow\left(x+1\right)^2=\left(\pm4\right)^2\\ \Rightarrow\left[{}\begin{matrix}x+1=4\\x+1=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)

\(f,\left(x+1\right)^3=27\\ \Rightarrow\left(x+1\right)^3=3^3\\ \Rightarrow x+1=3\\ \Rightarrow x=3-1\\ \Rightarrow x=2\\ g,\left(x+1\right)^3=1^6\\ \Rightarrow\left(x+1\right)^3=1^3\\ \Rightarrow x+1=1\\ \Rightarrow x=1-1\\ \Rightarrow x=0\\ h,\left(2\cdot x-1\right)^3=125\\ \Rightarrow\left(2x-1\right)^3=5^3\\ \Rightarrow2x-1=5\\ \Rightarrow2x=5+1\\ \Rightarrow2x=6\\ \Rightarrow x=3\)