Question

已知b^2=ac,求a^2b^2c^2/a^3+b^3+c^3*1/a^3+1/b^3+1/c^3的值

Answer 1

[(a^2b^2c^2)/(a^3+b^3+c^3)]*[1/a^3+1/b^3+1/c^3]

=(a^2b^2c^2)(1/a^3+1/b^3+1/c^3)/(a^3+b^3+c^3)

=[(b^2c^2/a)+(a^2c^2/b)+(a^2b^2/c)]/(a^3+b^3+c^3)

已知b^2=ac,(ac)^2=b^4,带入上式

=[ac*c^2/a+b^4/b+a^2*ac/c]/(a^3+b^3+c^3)

=(c^3+b^3+a^3)/(a^3+b^3+c^3)

=1