giai phuong trinh: \(\sqrt{2x^2-1}+\sqrt{x^2-3x-2}=\sqrt{2x^2+2x+3}+\sqrt{x^2-x-1}\)
Những câu hỏi liên quan
Giai phuong trinh ; 2\(\sqrt{x^2-x}-2\sqrt{x}\sqrt{2x-1}+3x=1\)
giai phuong trinh: \(\sqrt[3]{x^2+4x+3}+\sqrt[3]{4x^2-9x-3}=\sqrt[3]{3x^2-2x+2}+\sqrt[3]{2x^2-3x-2}\)
giai cac phuong trinh
a)\(2x^4+5x^3+x^2+5x+2=0\)
b)\(\sqrt{x-1}-\sqrt[3]{2-x}=1\)
c)\(x-\sqrt{x}+1=\sqrt{2x^2-30x+2}\)
d)\(2x^2+3x+7=\left(x-5\right)\sqrt{2x^2+1}\)
e)\(\sqrt{x-2}+\sqrt{4-x}=2x^2-5x-1\)
Giai phuong trinh
\(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-2\sqrt{2x-5}}=2\sqrt{2}\)
Giai phuong trinh :\(\sqrt{2-x^2+2x}+\sqrt{-x^2-6x+8}=1+\sqrt{3}\)
Giai phuong trinh \(\sqrt{2x^2+8x+6}+\sqrt{x^2-1}=2x+2\)
\(\sqrt{x+2+3\sqrt{ }2x-5}+\sqrt{x-2-\sqrt{ }2x-5}=2\sqrt{2}\) 2\(\sqrt{2}\) giai phuong trinh
giai phuong trinh \(\sqrt{\frac{x+7}{x+1}}+8=2x^2+\sqrt{2x-1}\)
ĐKXĐ: \(x\ge\frac{1}{2}\)
Đề \(\Rightarrow\sqrt{\frac{x+7}{x+1}}-\sqrt{3}+8-2x^2-\left(\sqrt{2x-1}-\sqrt{3}\right)=0\)
Nhân liên hợp ta được:
\(\frac{\left(\sqrt{\frac{x+7}{x+1}}-\sqrt{3}\right)\left(\sqrt{\frac{x+7}{x+1}}+\sqrt{3}\right)}{\sqrt{\frac{x+7}{x+1}}+\sqrt{3}}+2\left(4-x^2\right)-\frac{\left(\sqrt{2x-1}-\sqrt{3}\right)\left(\sqrt{2x+1}+\sqrt{3}\right)}{\sqrt{2x+1}+\sqrt{3}}=0\)
\(\Rightarrow\frac{\frac{x+7}{x+1}-3}{\sqrt{\frac{x+7}{x+1}}+\sqrt{3}}+2\left(4-x^2\right)-\frac{2x-1-3}{\sqrt{2x+1}+\sqrt{3}}=0\)
\(\Rightarrow\frac{\frac{-2x+4}{x+1}}{\sqrt{\frac{x+7}{x+1}}+\sqrt{3}}+2\left(2-x\right)\left(2+x\right)-\frac{2x-4}{\sqrt{2x+1}+\sqrt{3}}=0\)
\(\Rightarrow\left(x-2\right)\left[\frac{-2}{\left(x+1\right)\left(\sqrt{\frac{x+7}{x+1}}+\sqrt{3}\right)}-2\left(2+x\right)-\frac{2}{\sqrt{2x+1}+\sqrt{3}}\right]=0\)
mà \(-\frac{2}{\left(x+1\right)\left(\sqrt{\frac{x+7}{x+1}}+\sqrt{3}\right)}-2\left(2+x\right)-\frac{2}{\sqrt{2x+1}+\sqrt{3}}< 0\)
=> x - 2 = 0 => x = 2
Vậy x = 2
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giai phuong trinh
x2+2x+2=3x\(\sqrt{x+1}\)
ĐKXĐ: \(x\ge-1\)
Đặt \(\sqrt{x+1}=y\ge0\)
\(x^2+2x+2=3x\sqrt{x+1}\Leftrightarrow x^2+2\left(x+1\right)=3x\sqrt{x+1}\Leftrightarrow x^2+2y^2=3xy\)
\(\Leftrightarrow x^2-3xy+2y^2=0\Leftrightarrow x^2-xy-2xy+2y^2=0\Leftrightarrow x\left(x-y\right)-2y\left(x-y\right)=0\)
\(\Leftrightarrow\left(x-2y\right)\left(x-y\right)=0\Leftrightarrow\orbr{\begin{cases}x=2y\\x=y\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\sqrt{x+1}\\x=\sqrt{x+1}\end{cases}}\)
Đến đây đơn giản rồi bạn giải từng trường hợp là ra
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