GPT:
1, \(6x^2+10x-92+\sqrt{\left(x+70\right)\left(2x^2+4x+16\right)}=0\)
2,\(x+3+\sqrt{1-x^2}=3\sqrt{x+1}+\sqrt{1-x}\)
1.Cho a+b+c=1 và \(0\le\left|a\right|,\left|b\right|,\left|c\right|\le1\). CMR: \(a^4+b^5+c^6\le2\)
2.GPT: \(\sqrt{5x^2+6x+5}=\frac{64x^3+4x}{5x^2+6x+6}\)
3.Cho a,b,c tm: \(\sqrt{x^2+y^2}+\sqrt{y^2+z^2}+\sqrt{z^2+x^2}=6\)
TÌM MIN của : \(M=\frac{x^2}{y+z}+\frac{y^2}{z+x}+\frac{z^2}{x+y}\)
GPT
\($x^4+\left(x+1\right)\left(5x^2-6x-6\right)=0$\)
gpt:\(\sqrt{3x^2+6x+4}+\sqrt{2x^2+4x+11}=\left(1-x\right)\left(x+3\right)\)
\(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+21}=5-x^2-2x\)
\(\sqrt{x^2-x+2}+\sqrt{x^2-3x+6}=2x\)
GPT : \(x^2+6x+2=\left(2x+x\right)\sqrt{x^2+5}\)
GPT
\(x^4+\left(x+1\right)\left(5x^2-6x-6\right)=0\)
Tìm GTNN:
a, \(\frac{4x^2-6x+1}{\left(2x-1\right)^2}\)
b, \(\frac{\left(x+10\right)^2}{x}\)vs x>0
\(a,3x^3+6x^2-4x=0\)
\(b,\left(x+1\right)^3-x+1=\left(x-1\right)\left(x-2\right)\)
\(c,\left(x^2+x+1\right)^2=\left(4x-1\right)^2\)
\(d,\left(2x^2+3\right)^2-10x^3-15x=0\)
Cho đề \(\hept{\begin{cases}2y^2-x^2=1\\2\left(x^3-y\right)=y^3-x\end{cases}\Leftrightarrow}\)\(\hept{\begin{cases}2\left(y^2+1\right)-\left(x^2+1\right)=2\\x\left(2x^2+1\right)-y\left(y^2+2\right)=0\end{cases}}\)
đặt \(a=y^2+1,b=x^2+1\)
\(\Leftrightarrow\hept{\begin{cases}2a-b=2\\x\left(2b-1\right)-y\left(a+1\right)=0\end{cases}\Leftrightarrow\hept{\begin{cases}b=2a-2\\x\left(4a-5\right)-ya-y=0\end{cases}}}\Leftrightarrow\hept{\begin{cases}b=2a-2\\a=\frac{5x+y}{4x-y}\end{cases}\Leftrightarrow\hept{\begin{cases}b=\frac{2x+4y}{4x-y}\\a=\frac{5x+y}{4x-y}\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}y^2+1=\frac{5x+y}{4x-y}\left(1\right)\\x^2+1=\frac{2x+4y}{4x-y}\left(2\right)\end{cases}}\)
pt(1)-pt(2),ta dc:\(\left(x-y\right)\left(\frac{3}{4x-y}+x+y\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}x=y\left(3\right)\\\frac{3}{4x-y}+x+y=0\left(4\right)\end{cases}}\)
CM:PT (4) vô nghiệm giúp mình nha!Và xem lại nếu mình có lm sai hay thiếu đk j đó hãy chỉ giúp mình nha!!!Hoặc pt(4) có nghiệm thì hãy giải giúp mình luôn nha!Thanks