ĐKXĐ: \(x\ge\dfrac{3}{2}\)
\(\sqrt{2x-3+2\sqrt{2x-3}+1}+\sqrt{2x-3+2.4.\sqrt{2x-3}+16}=5\)
\(\Leftrightarrow\sqrt{\left(\sqrt{2x-3}+1\right)^2}+\sqrt{\left(\sqrt{2x-3}+4\right)^2}=5\)
\(\Leftrightarrow\sqrt{2x-3}+1+\sqrt{2x-3}+4=5\)
\(\Leftrightarrow2\sqrt{2x-3}=0\)
\(\Leftrightarrow2x-3=0\Rightarrow x=\dfrac{3}{2}\)
Giải pt
\(\sqrt{2x-2+2\sqrt{2x-3}}+\sqrt{2x+13+8\sqrt{2x-3}}=5\)
1. So sánh:
\(\sqrt{13}-\sqrt{12}\)và \(\sqrt{7}-\sqrt{6}\)
2. Giải pt:
\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
Giải pt
\(\sqrt{2x^2+6x-8}+\sqrt{2x^2+4x-6}-3\sqrt{x+4}=3\sqrt{x+3}+1\)
Giải PT: \(\sqrt{2x^2-9x+4}+3\sqrt{2x-1}=\sqrt{2x^2+21x-11}\)
Giải PT: \(\sqrt{2x^2-9x+4}+3\sqrt{2x-1}=\sqrt{2x^2+21x-11}\)
Giải PT: \(\sqrt{2x+3+\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
Giải PT: \(\sqrt{2x+3+\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
Giải PT: \(\sqrt{2x+3\sqrt{x+2}}+\sqrt{2x+2-\sqrt{x+2}}=1+2\sqrt{x+2}\)
Giải pt : a) \(\sqrt[3]{x^2-1}+x=\sqrt{x^3-1}\)
b) \(\sqrt{2x^2+3x+5}+\sqrt{2x^2-3x+5}=3x\)
c) \(2x^2-11x+2x=3\sqrt[3]{4x-4}\)
