a, ĐK: \(x=2017\)

\(\sqrt{x-2017}>\sqrt{2017-x}\)

\(\Leftrightarrow\left\{{}\begin{matrix}2017-x\ge0\\x-2017>2017-x\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le2017\\x>2017\end{matrix}\right.\)

\(\Rightarrow S=\varnothing\)

b, \(\dfrac{2x^2-3x+4}{x^2+3}>2\)

\(\Leftrightarrow2x^2-3x+4>2x^2+6\)

\(\Leftrightarrow x< -\dfrac{2}{3}\)

\(\Rightarrow S=\left(-\infty;-\dfrac{2}{3}\right)\)

c, ĐK: \(x\le2\)

\(3-2x+\sqrt{2-x}< x+\sqrt{2-x}\)

\(\Leftrightarrow3-2x+\sqrt{2-x}< x+\sqrt{2-x}\)

\(\Leftrightarrow3x>3\)

\(\Leftrightarrow x>1\)

\(\Rightarrow S=(1;2]\)

\(x^4+\sqrt{x^2+2017}=2017\)

\(\Leftrightarrow x^4+x^2+\frac{1}{4}=x^2+2017-\sqrt{x^2+2017}+\frac{1}{4}\)

\(\Leftrightarrow\left(x^2+\frac{1}{2}\right)^2=\left(\sqrt{x^2+2017}-\frac{1}{2}\right)^2\)

\(\Leftrightarrow x^2+\frac{1}{2}=\sqrt{x^2+2017}-\frac{1}{2}\)(vì \(\sqrt{x^2+2017}>\frac{1}{2}\))

\(\Leftrightarrow x^2-\sqrt{x^2+2017}+1=0\)

\(\Leftrightarrow\left(x^2+2017-\sqrt{x^2+2017}+\frac{1}{4}\right)=\frac{8065}{4}\)

\(\Leftrightarrow\left(\sqrt{x^2+2017}-\frac{1}{2}\right)^2=\frac{8065}{4}\)

\(\Leftrightarrow\sqrt{x^2+2017}=\frac{\sqrt{8065}+1}{2}\)

\(\Leftrightarrow x^2=\frac{\left(\sqrt{8065}+1\right)^2}{4}-2017\)

\(\Leftrightarrow\orbr{\begin{cases}x=\sqrt{\frac{\left(\sqrt{8065}+1\right)^2}{4}-2017}\\x=-\sqrt{\frac{\left(\sqrt{8065}+1\right)^2}{4}-2017}\end{cases}}\)

Cảm ơn bạn nha

ĐK: \(0\le x,y\le2017\)

*Ta thấy x=y=0 là 1 nghiệm của hpt.

*Với x,y\(\ne0\),trừ hai pt , ta được:

\(\sqrt{x}-\sqrt{y}-\left(\sqrt{2017-x}-\sqrt{2017-y}\right)=0\)

\(\Leftrightarrow\dfrac{x-y}{\sqrt{x}+\sqrt{y}}-\dfrac{2017-x-\left(2017-y\right)}{\sqrt{2017-x}+\sqrt{2017-y}}=0\)

\(\Leftrightarrow\left(x-y\right)\left[\dfrac{1}{\sqrt{x}+\sqrt{y}}+\dfrac{0}{\sqrt{2017-x}+\sqrt{2017-y}}\right]=0\)

\(\Rightarrow x=y\)(Vì \(\dfrac{1}{\sqrt{x}+\sqrt{y}}+\dfrac{0}{\sqrt{2017-x}+\sqrt{2017-y}}>0\forall0< x,y\le2017\))

Thay vào \(\sqrt{x}+\sqrt{2017-y}=\sqrt{2017}\), ta được:

\(\sqrt{x}+\sqrt{2017-x}=\sqrt{2017}\)

\(\Leftrightarrow x+2017-x+2\sqrt{-x^2+2017x}-2017=0\)

\(\Leftrightarrow x=0\)(KTM).

Vậy hpt có nghiệm là (0;0).

Đúng không ạ?

\(\left\{{}\begin{matrix}2017-x=2017+y-2y\sqrt{2017}\\2017-y=2017+y-2x\sqrt{2017}\end{matrix}\right.\)

Trừ 2 vế ta có:

\(\Rightarrow y-x=y-x-2\sqrt{2017}\left(y-x\right)\)

\(\Rightarrow\left(y-x\right)\left(1-1+2\sqrt{2017}\right)=0\)

\(\Rightarrow x=y\)

thay vào hệ đầu

từ a+b=3 => b=3-a

mặt khác: \(a^3-b^2=-3\)

=>\(a^3-\left(3-a\right)^2+3=0\)

\(\Rightarrow a^3-9+6a-a^2+3=0\)

\(\Rightarrow a^3-a^2+6a-6=0\)

\(\Rightarrow a^2\left(a-1\right)+6\left(a-1\right)=0\)

\(\Rightarrow\left(a^2+6\right)\left(a-1\right)=0\)

\(\Rightarrow\hept{\begin{cases}a^2+6=0\\a-1=0\end{cases}\Rightarrow\hept{\begin{cases}a^2=-6\\a=1\end{cases}}}\)

=>a=1 vì \(a^2\ge0\)

=>\(\sqrt[3]{x-2}=1\)

\(\Rightarrow x-2=1\Rightarrow x=3\)

Vậy x=3

b) ta có: Đặt :\(\sqrt[3]{x-2}=a;\)    Đk: \(x\ge-1\)

                \(\sqrt{x+1}=b;b\ge0\)

ta có:\(\hept{\begin{cases}a+b=3\\a^3-b^2=-3\end{cases}}\)

đến đây dùng pp thế là đc rồi nhé!

thế như nào bạn mình hơi ngu