Tim 3 so nguyen to lien tiep x, y, z ( voi x < y < z ) sao cho so A=\(x^2\)+\(y^2\)+\(z^2\)la mot so nguyen to.
Tim 3 so nguyen to lien tiep x,y,z (x<y<z) thoa man A = x^2 + y^2 + z^2 la so nguyen to
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).
CMR:neu so nguyen to x,y,z >3 thi:x^2+y^2+z^2 la hop so?
Cho x,y,z la 3 so nguyen duong, nguye to cung nhau thoa man (x-z)(y-z)=z^2. Chung minh tich xyz la so chinh phuong
Giai nhanh jum mik nha dg can gap
Cho x<y<z la ba so doi mot nguyen to cung nhau va tao thanh mot bo ba so Py-ta-go .Biet z=41 va x chia het cho 9 . Khi do ta co x la : ......... va y la:..................
thằng Tôi Ghét Cậu Phạm Tuấn Kiệt tốn giấy thế
cho x,y,z la cac so huu ti duong thoa man x+1/yz y +1/xz z+1/xy la cac so nguyen tim gia tri lon nhat cua bieu thuc A=x+y^2+z^3
1. tim cac cap so nguyen duong (x, y) sao cho:
2 x3 + xy = 11
2. tim cac cap so nguyen duong (x, y, z)sao cho:
x + y + z = x*y*z
3. tim x thuoc z, biet;
|x| = -2003
|x| = |-2003|
minh dang can gap lam. chieu mai phai nop rui
Cho x,y,z la cac so nguyen duong thoa man 1/x + 1/y + 1/z = 2015.
Tim GTLN cua bieu thuc P=x+y/x^2+y^2 + y+z/y^2+z^2 + z+x/z^2+x^2
Áp dụng bất đẳng thức cho ba số \(x,y,z\in Z^+\), ta được
\(x^2+y^2\ge2xy\) \(\Rightarrow\) \(\frac{x+y}{x^2+y^2}\le\frac{x+y}{2xy}\) \(\left(1\right)\)
\(y^2+z^2\ge2yz\) \(\Rightarrow\) \(\frac{y+z}{y^2+z^2}\le\frac{y+z}{2yz}\) \(\left(2\right)\)
\(z^2+x^2\ge2xz\) \(\Rightarrow\) \(\frac{z+x}{z^2+x^2}\le\frac{z+x}{2xz}\) \(\left(3\right)\)
Cộng từng vế của \(\left(1\right);\) \(\left(2\right)\) và \(\left(3\right)\) ta được \(\frac{x+y}{x^2+y^2}+\frac{y+z}{y^2+z^2}+\frac{z+x}{z^2+x^2}\le\frac{x+y}{2xy}+\frac{y+z}{2yz}+\frac{z+x}{2xz}=\frac{1}{2y}+\frac{1}{2x}+\frac{1}{2z}+\frac{1}{2y}+\frac{1}{2x}+\frac{1}{2z}\)
\(\Leftrightarrow\) \(P\le\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2015\)
Dấu \("="\) xảy ra khi và chỉ khi \(x=y=z=\frac{3}{2015}\)
Vậy, \(P_{max}=2015\) \(\Leftrightarrow\) \(x=y=z=\frac{3}{2015}\)
tim hai so huu ti x,y sao cho phan so dai dien co mau la 13 va cac tu la 2 so nguyen le lien tiep va x<\(\frac{4}{5}\)<y