\(a+b=1\Leftrightarrow b=1-a\)
\(LINH=2\left(a^3+b^3\right)-3\left(a^2+b^2\right)\)
\(=2\left[a^3+\left(1-a\right)^3\right]-3\left[a^2+\left(1-a\right)^2\right]\)
\(=2\left(a^3+1-3a+3a^2-a^3\right)-3\left(a^2+1-2a+a^2\right)\)
\(=2a^3+2-6a+6a^2-2a^3-3a^2-3+6a+3a^2\)
\(=\left(2a^3-2a^3\right)+\left(3a^2-3a^2\right)+\left(2-3\right)+\left(6a-6a\right)+\left(6a^2-3a^2\right)\)
\(=0+0-1+0+3a^2\)
\(=3a^2-1\)
ta có: 2(a3 + b3) - 3(a2 + b2)
= 2(a + b)(a2 - ab + b2) - 3a2 - 3b2
=2(a2 - ab + b2) - 3a2 - 3b2
= 2a2 - 2ab + 2b2 - 3a2 - 3b2
= -a2 - 2ab - b2
= -(a2 + 2ab + b2)
=-(a + b)2
= -(1)2 = -1
