Các câu hỏi tương tự
Giải pt và bpt sau:
a)\(\sqrt{x-2\sqrt{x-1}}\)=\(\sqrt{2}\)
b)\(\dfrac{4}{3}\sqrt{16\left(2-2x\right)^3}>24\)
B1:Giải bpt sau:left(sqrt{13}-sqrt{2x^2-2x+5}-sqrt{2x^2-4x+4}right).left(x^6-x^3+x^2-x+1right)ge0B2:Cho a;b;c0 thỏa mãn a+b+cfrac{1}{a}+frac{1}{b}+frac{1}{c}.CMR 3left(a+b+cright)gesqrt{8a^2+1}+sqrt{8b^2+1}+sqrt{8c^2+1}B3:giải pt nghiệm nguyên sau : 6left(y^2-1right)+3left(x^2+y^2z^2right)+2left(z^2-9xright)0
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B1:Giải bpt sau:\(\left(\sqrt{13}-\sqrt{2x^2-2x+5}-\sqrt{2x^2-4x+4}\right).\left(x^6-x^3+x^2-x+1\right)\ge0\)
B2:Cho a;b;c>0 thỏa mãn \(a+b+c=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\).CMR \(3\left(a+b+c\right)\ge\sqrt{8a^2+1}+\sqrt{8b^2+1}+\sqrt{8c^2+1}\)
B3:giải pt nghiệm nguyên sau : \(6\left(y^2-1\right)+3\left(x^2+y^2z^2\right)+2\left(z^2-9x\right)=0\)
Giải bpt: \(\sqrt{x^2+x}+\sqrt{x-2}\ge\sqrt{3\left(x^2-2x-2\right)}\)
giải các phương trình cô tỉ sau
1) \(\sqrt{x+1}-\sqrt{\frac{x+1}{x}}-1=0\)
2) \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^3+2\)
3) \(\sqrt{1+\sqrt{2x-x^2}}+\sqrt{1-\sqrt{2x-x^2}}=2\left(x-1\right)^4\left(2x^2-4x+1\right)\)
25 tháng 11 2023 lúc 20:36
Giải hpt sau:a)left{{}begin{matrix}2left(x^2-2xright)+sqrt{y+1}03left(x^2-2xright)-2sqrt{y+1}+70end{matrix}right.b)left{{}begin{matrix}5left|x-1right|-3left|y+2right|72sqrt{4x^2-8x+4}+5sqrt{y^2+4y+4}13end{matrix}right.c)left{{}begin{matrix}dfrac{3x}{x+1}-dfrac{2}{y+4}4dfrac{2x}{x+1}-dfrac{5}{y+4}9end{matrix}right.d)left{{}begin{matrix}dfrac{x+1}{x-1}+dfrac{3y}{y+2}7dfrac{2}{x-1}-dfrac{5}{y+2}4end{matrix}right.
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Giải hpt sau:
a)\(\left\{{}\begin{matrix}2\left(x^2-2x\right)+\sqrt{y+1}=0\\3\left(x^2-2x\right)-2\sqrt{y+1}+7=0\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}5\left|x-1\right|-3\left|y+2\right|=7\\2\sqrt{4x^2-8x+4}+5\sqrt{y^2+4y+4}=13\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}-\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\dfrac{x+1}{x-1}+\dfrac{3y}{y+2}=7\\\dfrac{2}{x-1}-\dfrac{5}{y+2}=4\end{matrix}\right.\)
Giải phương trình:
1: \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^2+2\)
2: \(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{16x-4x^2-15}\)
Giải các phương trình sau:
a) \(\sqrt{2x-1}+\sqrt{x-1}=5\)
b) \(x^2+2x+7=3\sqrt{\left(x^2+1\right).\left(x+3\right)}\)
1 tháng 10 2021 lúc 13:12
giải phương trình \(\left(\sqrt{x+3}-\sqrt{x+1}\right).\left(x^2+\sqrt{x^2+4x+3}\right)=2x\)
Bleft(frac{xsqrt{x}+x+sqrt{x}}{xsqrt{x}-1}-frac{sqrt{x}+3}{1-sqrt{x}}right).frac{x-1}{2x+sqrt{x}-1} ĐKXĐ: ...frac{left(xsqrt{x}+x+sqrt{x}right)left(1-sqrt{x}right)-left(sqrt{x}+3right)left(xsqrt{x}-1right)}{left(xsqrt{x}-1right)left(1-sqrt{x}right)}.frac{x-1}{2x+2sqrt{x}-sqrt{x}-1}frac{xsqrt{x}+x+sqrt{x}-x^2-xsqrt{x}-x-x^2+sqrt{x}-3xsqrt{x}+3}{left(xsqrt{x}-1right)left(1-sqrt{x}right)}.frac{x-1}{2sqrt{x}left(sqrt{x}+1right)-left(sqrt{x}+1right)}frac{-3xsqrt{x}+2sqrt{x}-2x^2+3}{left(xsqrt{x}-1ri...
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\(B=\left(\frac{x\sqrt{x}+x+\sqrt{x}}{x\sqrt{x}-1}-\frac{\sqrt{x}+3}{1-\sqrt{x}}\right).\frac{x-1}{2x+\sqrt{x}-1}\) ĐKXĐ: ...
\(=\frac{\left(x\sqrt{x}+x+\sqrt{x}\right)\left(1-\sqrt{x}\right)-\left(\sqrt{x}+3\right)\left(x\sqrt{x}-1\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{2x+2\sqrt{x}-\sqrt{x}-1}\)
\(=\frac{x\sqrt{x}+x+\sqrt{x}-x^2-x\sqrt{x}-x-x^2+\sqrt{x}-3x\sqrt{x}+3}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{2\sqrt{x}\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)}\)
\(=\frac{-3x\sqrt{x}+2\sqrt{x}-2x^2+3}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{3-3x\sqrt{x}+2\sqrt{x}-2x^2}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{3\left(1-x\sqrt{x}\right)+2\sqrt{x}\left(1-x\sqrt{x}\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(2\sqrt{x}+3\right)\left(1-x\sqrt{x}\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{-2\sqrt{x}-3}{1-\sqrt{x}}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{-2\sqrt{x}-3}{1-\sqrt{x}}.\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2\sqrt{x}-1}\)
\(=\frac{2\sqrt{x}+3}{2\sqrt{x}-1}\)