Question

x的y次等于y的x次,y等于9x求y

Answer 1

x^y=y^x

x^(9x)=(9x)^x

(x^9)^x=(9x)^x

x^9=9x

x(x^8 -9)=0

x(x^4+3)(x²+√3)[x+3^(1/4)][x-3^(1/4)]=0

x^4+3、x²+√3均恒>0,因此只有

x=0 x=-3^(1/4) x=3^(1/4)

x=0时,y=9x=0

x=-3^(1/4)时,y=9x=9×[-3^(1/4)]=-3^(2+1/4)=-3^(9/4)

x=3^(1/4)时,y=9x=9×3^(1/4)=3^(2+1/4)=3^(9/4)