Các câu hỏi tương tự
Cho x,y biết \(\left(x+\sqrt{1+y^2}\right)\left(y+\sqrt{1+x^2}\right)=1\)
CMR \(x\left(\sqrt{1+x^2}\right)\left(y+\sqrt{1+y^2}\right)=1\)
\(\frac{\sqrt{x}\left(\sqrt{x}-2\right)+\sqrt{y}\left(\sqrt{y}+2\right)-2\sqrt{xy}+1}{\sqrt{x}\left(\sqrt{x}-2\sqrt{y}\right)+\left(\sqrt{y}+1\right)\left(\sqrt{y}-1\right)}\)
Bài toán :
Cho \(\left(x+\sqrt{y^2+1}\right)\left(y+\sqrt{x^2+1}\right)=1\)
CMR : \(\left(x+\sqrt{x^2+1}\right)\left(y+\sqrt{y^2+1}\right)=1\)
Cho các số thực x,y thỏa mãn : \(\left(x+\sqrt{1+y^2}\right)\left(y+\sqrt{1+x^2}\right)=1\)
cmr: \(\left(x+\sqrt{1+x^2}\right)\left(y+\sqrt{1+y^2}\right)=1\)
Cho x,y,z>0 và xy+yz+zx=1
a, tính giá trị biểu thức:
\(P=x\sqrt{\frac{\left(1+y^2\right)\left(1+z^2\right)}{1+x^2}}+y\sqrt{\frac{\left(1+x^2\right)\left(1+z^2\right)}{1+y^2}}+z\sqrt{\frac{\left(1+x^2\right)\left(1+y^2\right)}{1+z^2}}\)
b, CMR:
\(\frac{x}{1+x^2}+\frac{y}{1+y^2}+\frac{z}{1+z^2}=\frac{2xy}{\sqrt{\left(1+x^2\right)\left(1+y^2\right)\left(1+z^2\right)}}\)
1,\(\left(x+\sqrt{x^2+1}\right)\left(y+\sqrt{y^2+4}\right)=2\). CMR: 2x +y =0
2,\(\left(x+\sqrt{x^2+9}\right)\left(y+\sqrt{y^2}+4\right)=6\). CMR 2x+3y=0
12 tháng 1 2022 lúc 22:34
1,Ghpt:\(\left\{{}\begin{matrix}x^2+3y+1=\left(x+3\right)\sqrt{y^2+1}\\\sqrt{2x\left(x+y\right)^3}+y\sqrt{2\left(x^2+y^2\right)}=3\left(x^2+y^2\right)\end{matrix}\right.\)
2,Cho a,b,c,d∈Z tm:\(a^2+b^2+c^2=d^2\)
CMR:\(abc⋮4\) (xét chẵn lẻ)
Cho ba số dương x,y,z thõa mãn điều kiện : \(xy+yz+xz=1\)
CMR:\(x\sqrt{\frac{\left(1+y^2\right)\left(1+z^2\right)}{1+x^2}}+y\sqrt{\frac{\left(1+z^2\right)\left(1+x^2\right)}{1+y^2}}+z\sqrt{\frac{\left(1+x^2\right)\left(1+y^2\right)}{1+z^2}}=2\)
Cho x,y dương thỏa mãn \(\sqrt{x}+\sqrt{y}-2>=0\)
CMR \(xy\left(\sqrt{x}+\sqrt{y}-2\right)+x^2\left(\sqrt{x}-1\right)+y^2\left(\sqrt{y}-1\right)>=0\)