Question

已知2倍x的立方=3倍y的立方=4倍z的立方,且1/x+1/y+1/z=1

Answer 1

设2x^3=3y^3=4z^3=k

x=(k/2)^(1/3),y=(k/3)^(1/3),z=(k/4)^(1/3)

代入2式

[2^(1/3)+3^(1/3)+4^(1/3)]/k^(1/3)=1

k^(1/3)=2^(1/3)+3^(1/3)+4^(1/3)

x=[2^(1/3)+3^(1/3)+4^(1/3)]/2^(1/3)

y=[2^(1/3)+3^(1/3)+4^(1/3)]/3^(1/3)

z=[2^(1/3)+3^(1/3)+4^(1/3)]/4^(1/3)

原式={[2^(1/3)+3^(1/3)+4^(1/3)]^2[2^(1/3)+3^(1/3)+4^(1/3)]}^(1/3)

=2^(1/3)+3^(1/3)+4^(1/3)