a² + b² chia hết cho ab

=>a² + b² chia hết cho a =>b chia hết cho a (1)

Và a² + b² chia hết cho b => a chia hết cho b (2)

Tử 1 và 2 => a =b

\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{5}\Rightarrow\dfrac{5y}{5xy}+\dfrac{5x}{5xy}=\dfrac{xy}{5xy}\)

\(\Rightarrow xy-5x-5y+25=25\)

\(\Rightarrow x\left(y-5\right)-5\left(y-5\right)=25\)

\(\Rightarrow\left(x-5\right)\left(y-5\right)=25\)

thiếu = 2017

SGK + SBT

Sao vậy nhỉ ?????

\(1^3+2^3+...+n^3=\left(1+2+...+n\right)^2=\left[\dfrac{\left(n+1\right)n}{2}\right]^2=9730^2\)

n(n+1)=19460=139.140

=> n= 139

139 là số nguyên tố không ? bạn?

\(A=\dfrac{18}{2-x}+\dfrac{2}{x}-9=2\left(\dfrac{9}{2-x}+\dfrac{1}{x}\right)-9=2M-9\)

Bunhiacopsky

\(\left(\sqrt{2-x}.\dfrac{3}{\sqrt{2-x}}+\sqrt{x}.\dfrac{1}{\sqrt{x}}\right)^2\le\left(2-x+x\right)\left(\dfrac{18}{2-x}+\dfrac{2}{x}\right)\)

\(M\ge\dfrac{16}{2}=8\)

\(B\ge2.8-9=7\)

B min =7 khi \(\dfrac{18}{2-x}=\dfrac{2}{x}\Rightarrow x=\dfrac{1}{5}\)

\(\left(\sqrt{1-x}.\dfrac{\sqrt{3}}{\sqrt{1-x}}+\sqrt{x}.\dfrac{2}{\sqrt{x}}\right)^2\le\left(1-x+x\right)\left(B\right)\)

\(\Rightarrow B\ge\left(\sqrt{3}+2\right)^2=7+4\sqrt{3}\)

Bmin = 7+4can 3

khi\(\dfrac{\sqrt{3}}{1-x}=\dfrac{2}{x}\Rightarrow x=\dfrac{2}{\sqrt{3}+2}\)