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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Prove that (xa / xb)1/ab (xb / xc)1/bc (xc / xa)1/ca = 1
Exponential formulas of multiplication and division can be used to simplify such expressions.
Answer: Value of the L.H.S. comes out to be 1 thus the identity holds true.
Go through the proof and understand the solvation of this expression.
Explanation:
L.H.S = (xa / xb)1/ab (xb / xc)1/bc (xc / xa)1/ca
On simplifying the L.H.S, we get:
(xa / xb)1/ab (xb / xc)1/bc (xc / xa)1/ca
⇒ (xa - b)1/ab (xb - c)1/bc (xc - a)1/ca
⇒ (x(a - b)/ab) (x(b - c)/bc) (x(c - a)/ca)
⇒ (x[(a - b)/ab] + [(b - c)/bc] + [(c - a)/ca])
⇒ x (ac - bc + ab - ca + bc - ab) / abc
⇒ x0 = 1
= R.H.S
Since, R.H.S = L.H.S, hence proved.
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