Question

已知非零实数a,b,c满足2a-3b+c=0,a-2b-2c=0,试求代数式a^2-2b^2-8c^分之ab+4bc+2

Answer 1

2a-3b+c=0,①

a-2b-2c=0,②

①-②×2,得,

b=-5c,

代人①,得,

a=-8c,

将a=-8c,b=-5c代人到代数式中,得,

a^2-2b^2-8c^分之ab+4bc+2ab

=(ab+4bc+2ab)/(a^2-2b^2-8c^2)

=(40c^2-20c^2+80c^2)/(64c^2-50c^2-8c^2)

=100c^2/6c^2

=50/3