\(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\)
Những câu hỏi liên quan
\(\sqrt{10x+1}\) + \(\sqrt{3x-5}\) = \(\sqrt{9x+4}\) + \(\sqrt{2x-2}\)
ĐK: \(x\ge\dfrac{5}{3}\)
\(pt\Leftrightarrow\left(\sqrt{10x+1}-\sqrt{9x+4}\right)+\left(\sqrt{3x-5}-\sqrt{2x-2}\right)=0\)
\(\Leftrightarrow\dfrac{x-3}{\sqrt{10x+1}+\sqrt{9x+4}}+\dfrac{x-3}{\sqrt{3x-5}+\sqrt{2x-2}}=0\)
\(\Leftrightarrow\left(x-3\right)\left(\dfrac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\dfrac{1}{\sqrt{3x-5}+\sqrt{2x-2}}\right)=0\)
Dễ thấy \(\dfrac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\dfrac{1}{\sqrt{3x-5}+\sqrt{2x-2}}>0\)
\(pt\Leftrightarrow x-3=0\)
\(\Leftrightarrow x=3\left(tm\right)\)
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\(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\)
\(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\left(ĐKXĐ:
x\ge\frac{5}{3}\right)\)
\(\Leftrightarrow\sqrt{10x+1}-\sqrt{9x+4}=\sqrt{2x-2}-\sqrt{3x-5}\)
\(\Leftrightarrow\frac{10x+1-\left(9x+4\right)}{\sqrt{10x+1}+\sqrt{9x+4}}=\frac{2x-2-\left(3x-5\right)}{\sqrt{2x-2}+\sqrt{3x-5}}\)
\(\Leftrightarrow\frac{x-3}{\sqrt{10x+1}+\sqrt{9x+4}}=\frac{3-x}{\sqrt{2x-2}+\sqrt{3x-5}}\)
\(\Leftrightarrow\left(x-3\right)\left(\frac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\frac{1}{\sqrt{2x-2}+\sqrt{3x-5}}\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}x=3\\\sqrt{10x+1}+\sqrt{3x-5}+\sqrt{9x+4}+\sqrt{2x-2}=0\left(vo.nghiem\right)\end{cases}}\)
\(\Leftrightarrow x=3\)
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Giải phương trình: \(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\)
Giải phương trình: \(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\)
ĐKXĐ: \(x\ge\dfrac{5}{3}\)
\(\sqrt{10x+1}-\sqrt{9x+4}+\sqrt{3x-5}-\sqrt{2x-2}=0\)
\(\Leftrightarrow\dfrac{x-3}{\sqrt{10x+1}+\sqrt{9x+4}}+\dfrac{x-3}{\sqrt{3x-5}+\sqrt{2x-2}}=0\)
\(\Leftrightarrow\left(x-3\right)\left(\dfrac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\dfrac{1}{\sqrt{3x-5}+\sqrt{2x-2}}\right)=0\)
\(\Leftrightarrow x-3=0\Rightarrow x=3\)
Do \(\dfrac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\dfrac{1}{\sqrt{3x-5}+\sqrt{2x-2}}>0\) \(\forall x\ge\dfrac{5}{3}\)
Vậy pt có nghiệm duy nhất \(x=3\)
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Giải bất phương trình: \(\sqrt{10x+1}+\sqrt{3x-5}\ge\sqrt{9x+4}+\sqrt{2x-2}\)
ĐKXĐ: \(x\ge\frac{5}{3}\)
\(\Leftrightarrow\sqrt{10x+1}-\sqrt{9x+4}+\sqrt{3x-5}-\sqrt{2x-2}\ge0\)
\(\Leftrightarrow\frac{x-3}{\sqrt{10x+1}+\sqrt{9x+4}}+\frac{x-3}{\sqrt{3x-5}+\sqrt{2x-2}}\ge0\)
\(\Leftrightarrow\left(x-3\right)\left(\frac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\frac{1}{\sqrt{3x-5}+\sqrt{2x-2}}\right)\ge0\)
\(\Leftrightarrow x-3\ge0\) (do ngoặc đằng sau luôn dương)
\(\Rightarrow x\ge3\)
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\(\sqrt{10x+1}+\sqrt{3x+5}=\sqrt{9x+4}+\sqrt{2x-2}\)
\(\sqrt{2x^2+x-1}+\sqrt{3x^2+x-1}=\sqrt{x^2+4x-3}-\sqrt{x^2-3x+4}\)
\(\frac{x^2}{\left(1+\sqrt{x+1}\right)^2}>x-4\)
giải phương trình \(\sqrt{10x+1}\)+\(\sqrt{3x-5}\)=\(\sqrt{9x-4}\)+ \(\sqrt{2x-2}\)
giải pt:
a,\(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{-4x^2+16x-15}\)
b,\(\left(9x-2\right)\sqrt{3x-1}+\left(10-9x\right)\sqrt{3-3x}-4\sqrt{-9x^2+12x-3}=4\)
c, \(\left(6x-5\right)\sqrt{x+1}-\left(6x+2\right)\sqrt{x-1}+4\sqrt{x^2-1}=4x-3\)
giải phương trình \(\sqrt{10x+1}\)+\(\sqrt{3x-5}\)=\(\sqrt{9x-4}\)+\(\sqrt{2x-2}\)
đề đungs \(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\). ĐK: \(x\ge\frac{5}{3}\)
\(\Leftrightarrow\)\(\sqrt{10x+1}-\sqrt{9x+4}+\sqrt{3x-5}-\sqrt{2x-2}=0\)
\(\Leftrightarrow\)\(\frac{10x+1-9x-4}{\sqrt{10x+1}+\sqrt{9x+4}}+\frac{3x-5-2x+2}{\sqrt{3x-5}+\sqrt{2x-2}}=0\)
\(\Leftrightarrow\)\(\left(x-3\right)\left(\frac{1}{\sqrt{10x+1}+\sqrt{9x+4}}+\frac{1}{\sqrt{3x-5}+\sqrt{2x-2}}\right)=0\)
\(\Leftrightarrow\)\(x=3\) ( nhan )