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प्रश्न
Prove the following:
(xa)b-c x (xb)c-a x (xc)a-b = 1
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उत्तर
L.H.S.
= (xa)b-c x (xb)c-a x (xc)a-b
= `x^("a"("b"-"c")) xx x^("b"("c"-"a")) xx x^("c"("a"-"b"))` .....(Using (am)n = amn)
= `x^("ab"-"ac") xx x^("bc"-"ab") xx x^("ac"-"bc")`
= `x^("ab"-"ac"+"bc"-"ab"+"ac"-"bc")` .....(Using am x an = am+n)
= x°
=1
= R.H.S
= Hence proved.
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