Question

3^x=4^y=5^z=60^p prove p(yx+xz+zy)=xyz

Answer 1

Step-by-step explanation:

Form a quadratic equation whose Roots are x,y,z

Now, let the equation be ax3+bx2+cx+d=0

So, Sum x+y+z=−b/a

xy+yz+xz=c/a

xyz=−d/a

If a=1 , equation will be x3−6x2+15x−14=0

So, x=2 is a root of equation : the equation can be written as (x−2)(x2−4x+7)=0

Since x2−4x+7=0 has imaginary roots which are 2+isqrt3 and 2−isqrt3

So, the only real solution for this equation is x=2

Hope this was helpful.