ĐK: \(0\le x\le7\)
\(2\sqrt{3}-\sqrt{7x-x^2}=0\Leftrightarrow2\sqrt{3}=\sqrt{7x-x^2}\Leftrightarrow12=7x-x^2\)
\(\Leftrightarrow x^2-7x+12=0\Leftrightarrow x^2-4x-3x+12=0\Leftrightarrow x.\left(x-4\right)-3.\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-4\right)=0\Leftrightarrow x=3\text{ hoặc }x=4\text{. Vậy S=}\left\{3;4\right\}\)
giải các pt sau
i)\(\left(1-\sqrt{2}\right)x^2-2\left(1+\sqrt{2}\right)x+1+3\sqrt{2}=0\)
ii)\(^{\left(6x^2-7x\right)^2-2\left(6x^2-7x\right)-3=0}\)
giải pt\(\sqrt[3]{7x+1}-\sqrt[3]{x^2-x-8}+\sqrt[3]{x^2-8x-1}=2\)
2. Giải PT:
a) \(\frac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}.\)
b) \(\sqrt{4x-20}+3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=4.\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0.\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6.\)
\(\text{Giải hệ pt :}\)
\(\hept{\begin{cases}\sqrt{x-2}-y\sqrt{y}=\sqrt{y-2}-x\sqrt{x}\\3x^2-y^2-xy-7x+y+5=0\end{cases}}\)
Giải pt: \(\sqrt{3x^2-7x+3}-\sqrt{x^2-2}=\sqrt{3x^2-5x-1}-\sqrt{x^2-3x+4}\)
Giải pt sau đây
\(\sqrt{x^2-x+19}+\sqrt{7x^2+8x+13}+\sqrt{13x^2+17x+7}-3\sqrt{3}x=6\sqrt{3}\)
giải pt \(\sqrt{3x^2-6x-6}=3\sqrt{\left(2-x\right)^5}+\left(7x-19\right)\sqrt{2-x}\)
Giải pt
(\(\sqrt{x+5}-\sqrt{x+2}\)) (\(1+\sqrt{x^2+7x+10}\)) = 3
Giải PT sau áp dụng bất đẳng thức
\(\sqrt{x^2-x+19}+\sqrt{7x^2+8x+13}+\sqrt{13x^2+17x+7}-3\sqrt{3}x=6\sqrt{3}\)
