Question

cho a+2b=1, a\(\ne\) 0

chứng minh  : \(a^3+8b^3+2ab-a^2-4b^2=0\)

Answer 1

a + 2b = 1 => 2b = 1 - a

Biến đổi VT:

\(a^3+8b^3+2ab-a^2-4b^2\)

\(=a\left(a^2+2b-a\right)+\left(2b\right)^3-\left(2b\right)^2\)

\(=a\left(a^2+1-a-a\right)+\left(2b\right)^2\left(2b-1\right)\)

\(=a\left(a^2-2a+1\right)+\left(1-a\right)^2\left(1-a-1\right)\)

\(=a\left(a-1\right)^2-a\left(1-a\right)^2\)

\(=a\left[\left(a-1\right)^2-\left(1-a\right)^2\right]\)

\(=a\left(a-1+1-a\right)\left(a-1-1+a\right)\)

\(=0\)(đpcm)