Cho 3 so x, y, z thoa man cac he thuc: \(\left(z-1\right)x-y=1\) va \(x+zy=2\)
Chmr: \(\left(2x-y\right)\left(z^2-z+1\right)=7\) va tim tat ca cac so nguyen x, y, z thoa man cac he thuc tren.
Cho bieu thuc \(P=\left(\dfrac{3}{x-1}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{1}{\sqrt{x}+1}\)
a.Neu dkxd va rut gon bieu thuc P
b.Tim cac gia tri cua x de \(P=\dfrac{5}{4}\)
c.Tim gia tri nho nhat cua bieu thuc :\(M=\dfrac{x+12}{\sqrt{x}-1}\cdot\dfrac{1}{P}\)
1) Cho bieu thuc: \(B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\left(x\ge0,x\ne16\right)\)
a) Cho bieu thuc A= \(\frac{\sqrt{x}+4}{\sqrt{x}+2}\) ; voi cac cua bieu thuc A va B da cho, hay tim cac gia tri cua x nguyen de gia tri cua bieu thuc B(A;-1) la so nguyen
Cho cac so thuc duong x,y,z thoa man :\(\sqrt{x^2+y^2}+\sqrt{y^2+z^2}+\sqrt{z^2+x^2=2015}\)
Tim ja tri nho nhat cua bieu thuc :\(T=\dfrac{x^2}{y+x}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}\)
1, Tinh gtri nho nhat cua bieu thuc A = \(\left|x-1\right|+\left|x-2\right|+..+\left|x-2020\right|\)
Chung minh bieu thuc sau ko phu thuoc vao gia tri cua x:
\(A=\dfrac{6x-\left(x+6\right)\sqrt{x}-3}{2\left(x-4\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}-\dfrac{3}{-2x+10\sqrt{x}-12}-\dfrac{1}{3\sqrt{3}-x-2}\)
cho bieu thuc
P\(\left(x\right)=\dfrac{20x^2+120x+180}{\left(3x+5\right)^2-4x^2}+\dfrac{5x^2-125}{9x^2-\left(2x+5\right)^2}-\dfrac{\left(2x+3\right)^2-x^2}{3\left(x^2+8x+15\right)}\)
Tim gia tri nguyen cua x de P(x) co gia tri nguyen
Cho P = \(\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\right)\): \(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{2}{x-1}\right)\)
a/ Tim DKXD va rut gon P
b/ Tim cac gia tri nguyen cua x de P co gia tri nguyen
cho x,y,z thỏa mãn \(x+y+z\le\dfrac{3}{2}\) . tìm GTNN của \(P=\dfrac{x\left(yz+1\right)^2}{z^2\left(xz+1\right)}+\dfrac{y\left(xz+1\right)^2}{y^2\left(xy+1\right)}+\dfrac{z\left(xy+1\right)^2}{x^2\left(yz+1\right)}\)
