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
參考答案: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+b^3+c^3]*[b^3c^3+a^3c^3+a^3b^3]/[a^3b^3c^3]
=[b^3c^3+a^3c^3+a^3b^3]/[abc(a^3+b^3+c^3]
=[b^3c^3+b^6+a^3b^3]/[b^3(a^3+b^3+c^3)]
=[c^3+b^3+a^3]/[a^3+b^3+c^3]
=1