\(\sqrt[3]{x+1}+\sqrt[3]{x-1}=\sqrt[3]{5x}\)
<=> \(\left(\sqrt[3]{x+1}+\sqrt[3]{x-1}\right)^3=5x\)
<=> \(\left(2x\right)^3-3\left(x+1\right)\left(x-1\right)2x=5x\)
<=> \(8x^3-6x\left(x^2-1\right)=5x\)
<=> \(8x^3-6x^3+6x-5x=0\)
<=> \(2x^3+x=0\)
<=> \(x\left(2x^2+1\right)=0\)
<=>\(\orbr{\begin{cases}x=0\\2x^2+1=0\end{cases}}\)
Mà \(2x^2\ge0\)=> \(2x^2+1\ge1>0\)
<=> x=0
\(S=\left\{0\right\}\)
giải pt: \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x+4}\)
giải pt sau
a)\(\sqrt{x^2-6x+9}=3\)
b)\(\sqrt{x+2\sqrt{x-1}}=2\)
c)\(\dfrac{\sqrt{5x-4}}{\sqrt{x+2}}=2\)
d)\(\sqrt{x-4}+\sqrt{x+1}=5\)
Help
giải pt \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{2x-3}}=\sqrt{3}\left(\frac{1}{\sqrt{4x-3}}+\frac{1}{\sqrt{5x-6}}\right)\)
Giải các PT sau:
a) \(\sqrt[3]{x+5}+\sqrt[3]{x+6}=\sqrt[3]{2x+11}\)
b) \(\sqrt[3]{x+1}+\sqrt[3]{x-1}=\sqrt[3]{5x}\)
Mọi người giúp mình với ạ!!!
Giải PT : \(x^2+\sqrt{2x+1}+\sqrt{x-3}=5x\left(1\right)\)
giải hệ PT: \(\hept{\begin{cases}\sqrt{3}x-y=1\\5x+\sqrt{2}y=\sqrt{3}\end{cases}}\)
giải pt: \(\sqrt{5x-1}+\sqrt[3]{9-x}=2x^2+3x-1\)
giải pt :
\(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
Ai dậy r giúp vs :33 1 câu cx đc nhé :v toàn giải pt hết nhé
1) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}.\)
2) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+18-\left(x+26\right)\sqrt{x-1}\)
3) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
4) \(\left(x+17\right)\sqrt{4-x}+\left(20-x\right)\sqrt{x+1}-9\sqrt{4-x}.\sqrt{x+1}=36\)
