\(\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\Rightarrow c=\frac{ab}{a+b}\)
\(a^2+b^2+c^2=\left(a+b\right)^2-2ab+\frac{a^2b^2}{\left(a+b\right)^2}=\frac{\left(a+b\right)^4-2ab\left(a+b\right)^2+a^2b^2}{\left(a+b\right)^2}\)
\(=\frac{\left[\left(a+b\right)^2-ab\right]^2}{\left(a+b\right)^2}\)
\(\Rightarrow\sqrt{a^2+b^2+c^2}=\left|\frac{\left(a+b\right)^2-ab}{a+b}\right|\) là số hữu tỉ.
cho x;y la hai so huu ti thoa man \(x^3+y^3=2x^2y^2\)cmr \(\sqrt{1-\frac{1}{xy}}\)la mot so huu ti
gia su a,b la 2 so huu ti duong va khong phai la binh phuong cua mot so huu ti
chung minh rang :neu x,y la hai so huu ti sao cho \(m=x\sqrt{a}+y\sqrt{b}\)la so huu ti thi m=0
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).
chứng minh \(\sqrt{\frac{1}{\left(a-b^2\right)}+\frac{1}{\left(b-c\right)^2}-\frac{1}{\left(c-a\right)^2}}\)la mot so huu ti
cho 3 so huu ti phan biet c/m
\(\sqrt{\frac{1}{\left(x-4\right)^2}+\frac{1}{\left(y-z\right)^2}+\frac{1}{\left(z-x\right)^2}}\) la so huu ti
Xet xem cac so a va b co the la so vo ti k neu
A)a+b va a-b la cac so huu ti
B)a-b va ab la cac so huu ti
cho truoc so huu ty m sao cho\(\sqrt[3]{m}\) la so vo ty ;Tim cac so huu ty a;b;c sao cho:\(a\sqrt[3]{m^2}+b\sqrt[3]{m}+c=0\)
cho a,b,c la cac so thuc duong thoa man 21ab+2bc+8ac <= 12
khi do gia ti nho nhat cua A=1/a+2/b +3/c
Cho \(\sqrt{a}+\sqrt{b}\) la so huu ti, a + b la so tu nhien. Chung minh \(\sqrt{a},\sqrt{b}\)la so tu nhien
