Giải phương trình:
1, $2x^{2}+2x+1=\sqrt{4x+1}$.
2, $\sqrt{x-2}+\sqrt{x-7}=\sqrt{x+5}+\sqrt{x+10}$.
3, $\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x-2}}=3$.
4, $\sqrt{2x+3}+\sqrt{x+1}=3x-16+2\sqrt{2x^{2}+5x+3}$.
5, $\sqrt[3]{x-2}+\sqrt[3]{x+3}=\sqrt[3]{2x+1}$.
6, $\sqrt{x-2}+\sqrt{4-x}=x^{2}-6x+11$.
7, $\sqrt{2x-1}=\frac{x^{2}+1}{2}$.
8, $\sqrt{x-2}+\sqrt{4-x}=2x^{2}-5x-1$.
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