\(600-\left(1+3+5+...+x\right)=375\)

\(\Rightarrow\dfrac{\left(x-1\right):2+1}{2}\left(x+1\right)=225\)

\(\Rightarrow\dfrac{x+1}{4}\left(x+1\right)=225\)

\(\Rightarrow\left(x+1\right)^2=900\)

\(\Rightarrow x+1=30\left(x>0\right)\)

\(\Rightarrow x=29\)

g) \(\dfrac{18}{\sqrt{7}+1}=\dfrac{18\left(\sqrt{7}-1\right)}{7-1}=3\left(\sqrt{7}-1\right)=3\sqrt{7}-3\) 

h) \(\dfrac{3}{2\sqrt{2}-\sqrt{5}}=\dfrac{3\left(2\sqrt{2}+\sqrt{5}\right)}{8-5}=2\sqrt{2}+\sqrt{5}\)

i) a > 0 ; a \(\ne b\) . Ta có : \(\dfrac{a\sqrt{a}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(a+b+\sqrt{ab}\right)}{\sqrt{a}-\sqrt{b}}=a+b+\sqrt{ab}\)

a) \(C\left(x\right)=-4x^3+2x^2-2\left(x^2-x^3\right)+2022\)  = \(-2x^3+2022\)

b) Bậc của đa thức : 3 ; hệ số cao nhất : -2 ; hệ số tự do : 2022

c) \(C\left(-x\right)=2x^3+2022\)

C(x) + C(-x) = 4044

2,5x + \(\dfrac{4}{7}=-1,5\)

\(\Leftrightarrow2,5x=-\dfrac{29}{14}\)

\(\Leftrightarrow x=-\dfrac{29}{35}\)

x là no của p/t : \(x^2+7x+12=0\Leftrightarrow\left(x+3\right)\left(x+4\right)=0\)  \(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-4\end{matrix}\right.\)

Với x = -3 \(\Rightarrow y=-4\) \(\Rightarrow x^2-y^2=9-16=-7\)

Với x = -4 => y = -3 (L) 

P/t \(\Leftrightarrow\sqrt[3]{x^2\left(x+2\right)}=x+2\)  

\(\Leftrightarrow\left(x+2\right)\left(\sqrt[3]{x^2}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\pm1\end{matrix}\right.\)

\(\dfrac{27^{10}+9^5}{9^{13}+27^2}=\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\)  = \(\dfrac{3^{30}+3^{10}}{3^{26}+3^6}=\dfrac{3^{10}\left(1+3^{20}\right)}{3^6\left(1+3^{20}\right)}=3^4=81\)

\(...=\dfrac{2^5.3^3.5^3}{2^6.3^6.2^2.5^2}=\dfrac{2^5.3^3.5^3}{2^8.3^6.5^2}=\dfrac{5}{2^3.3^3}\)  = \(\dfrac{5}{6^3}\)

... = \(4ab=4.2^8.3^{10}=2^{10}.3^{10}=6^{10}\)

ĐKXĐ : \(x\le3\)