\(C=\left(2n+1\right)^2-1\)
\(C=\left(2n+1-1\right)\left(2n+1+1\right)\)
\(C=2n\left(2n+2\right)\)
\(C=4n\left(n+1\right)⋮8\left(đpcm\right)\)
Các pạn giúp mk câu 1 thui nha!!! @lê thị hương giang, @Phạm Hoàng Giang, Trần Quốc Lộc, ...
Bài 1 : Ta có :
\(\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax+by\right)^2\)
\(\Leftrightarrow a^2x^2+a^2y^2+b^2x^2+b^2y^2=a^2x^2+2.ax.by+b^2y^2\)
\(\Leftrightarrow a^2x^2+a^2y^2+b^2x^2+b^2y^2-a^2x^2-2ax.by-b^2y^2=0\)
\(\Leftrightarrow a^2y^2+b^2x^2-2ax.by=0\)
\(\Leftrightarrow a^2y^2-2ay.bx+b^2x^2=0\)
\(\Leftrightarrow\left(ay-bx\right)^2=0\)
\(\Rightarrow ay=bx\left(đpcm\right)\)
\(\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax+by\right)^2\)
\(\Rightarrow\left(a^2+b^2\right)\left(x^2+y^2\right)-\left(ax+by\right)^2=0\)
\(\Rightarrow a^2x^2+a^2y^2+b^2x^2+b^2y^2-a^2y^2-2axby-b^2y^2=0\)
\(\Rightarrow a^2y^2-2axby+b^2x^2=0\)
\(\Rightarrow\left(ay\right)^2-2.ay.bx+\left(bx\right)^2=0\)
\(\Rightarrow\left(ay-bx\right)^2=0\)
\(\Rightarrow ay-bx=0\) ( đpcm )