Question

已知

x

3

=

y

1

=

z

2

，則

2x2-2y2+5z2

xy+yz+zx

=

 

．

Answer 1

分析：可以設(shè)

x

3

=

y

1

=

z

2

=k，則x=3k，y=k，z=2k．把這三個(gè)式子代入所要求的式子再進(jìn)行化簡(jiǎn)就得到式子的值．

解答：解：設(shè)

x

3

=

y

1

=

z

2

=k，
則x=3k，y=k，z=2k，
則

2x2-2y2+5z2

xy+yz+zx

=

18k2-2k2+20k2

3k2+2k2+6k2

=

36k2

11k2

=

36

11

．
故答案為

36

11

．

點(diǎn)評(píng)：掌握本題的設(shè)法，把多個(gè)未知數(shù)的問(wèn)題轉(zhuǎn)化為一個(gè)未知數(shù)的問(wèn)題．