Question

If x ^ 1/m = y^ 1/n = z ^1/p and xyz=1 then find m+n+p-8.

Answer 1

Answer:

x ^ 1/m = y^ 1/n = z ^1/p = k (say)

So

x = k^m

y = k^n

z = k^p

Now

xyz=1 gives

k^m ×k^n ×k^p = k^0

k^m+n+p = k^0

m+n+p = 0

So

m+n+p-8

= 0 - 8

= - 8

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