tim x thuoc N de bieu thuc sau co gia tri la so tu nhien: Q=\(\dfrac{\text{x}+1}{\text{x}-\sqrt{\text{x}}+1}\)
M = \(\frac{3\sqrt{x}}{\sqrt{x-3}}\)
Tìm x thuoc N de gia tri cua M la so tu nhien.
a)Tim tat ca cac so nguyen duong x, y , z thoa man: \(\frac{x+y\sqrt{2013}}{y+z\sqrt{2013}}\)la so huu ti, dong thoi x2 + y2+ z2 la so nguyen to.
b) Tim so tu nhien x, y thoa man: x(1+x+x2) = y(y-1).
\(M=\left(\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\frac{\sqrt{x}-2}{x-1}\right)N=\frac{\sqrt{x}+1}{\sqrt{x}}\) voi x>0 va x khac 1
a) tim gia tri bieu thuc cua N khi x = 25
b) rut gon S = M.N
c) tim m de S<-1
\(\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)
a,rut gon
b,tim x de p duong
c,tim x de p = -5/2
d,tim x de p thuoc z
e,tim x de p >9/2
P=\(\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{2\sqrt{x}}{\sqrt{x}+2}+\frac{2+5\sqrt{x}}{4-x}\)
a,rut gon
b,tim x de P duong
c,tim x de P=-5/2
d,tim x de p thuoc Z
rut gon roi tim x de p=-2 \(p=\left(\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{\sqrt{x}}{\sqrt{x}-1}\right):\frac{2}{\sqrt{x}+1}\)
a)\(\left(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+x\sqrt{x}}\right):\frac{2\left(x-2\sqrt{x}+1\right)}{x-1}\)
Rut gon
Tim x de B nguyen
1.Tim a de \(N=\frac{6}{M}\in Z\)biet \(M=\frac{a+2\sqrt{a}+1}{\sqrt{a}}\)
2.tim nghiem nguyen to cua pt:\(x^2-2y^3=1\)
3.Cho a, b,c la 3 canh cua tam giac.CM:\(a^2\left(b+c\right)+b^2\left(c+a\right)+c^2\left(a+b\right)\subseteq a^3+b^3+c^3\)
4.ve do thi ham so \(y=\sqrt{x^2-4x+4}-\sqrt{x^2+4x+4}\)dung do thi. tim GTLN,GTNN.