Question

已知

x

2

=

y

3

=

z

4

，求

xy+yz+3zx

x2+y2+z2

的值．

Answer 1

分析：先設(shè)

x

2

=

y

3

=

z

4

=k，可得x=2k，y=3k，z=4k，再把x、y、z的值都代入所求式子計(jì)算即可．

解答：解：設(shè)

x

2

=

y

3

=

z

4

=k，可得x=2k，y=3k，z=4k，
∴

xy+yz+3zx

x2+y2+z2

=

6k2+12k2+24k2

4k2+9k2+16k2

=

42

29

．

點(diǎn)評(píng)：本題考查了比例的性質(zhì)．解題的關(guān)鍵是先假設(shè)

x

2

=

y

3

=

z

4

=k，可得x=2k，y=3k，z=4k，降低計(jì)算難度．