Question

If 2x =5y =10z prove that 1÷x+1÷y=1÷z

Answer 1

Step-by-step explanation:

Let 2^x=5^y=10^z=K

2^x=K=2=K^1/2

5^y=K=5=K^1/5

10^z=K=10=k^1/10

consider, 10=2*5

K^1/z=K^1/x*K^1/z

K^1/z=K^1/x+K^1/z

therefore,1/x+1/y=1/z

hence,proved