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प्रश्न
Prove that:
`((x^a)/x^b)^(1/(ab))((x^b)/x^c)^(1/(bc))(x^c/x^a)^(1/(ca))=1`
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उत्तर
`(("x"^"a")/"x"^"b")^(1/("a""b"))(("x"^"b")/"x"^"c")^(1/("b""c"))("x"^"c"/"x"^"a")^(1/("c""a"))=1`
`"L"."H"."S".=``(("x"^"a")/"x"^"b")^(1/("a""b"))(("x"^"b")/"x"^"c")^(1/("b""c"))("x"^"c"/"x"^"a")^(1/("c""a"))`
`("x"^("a"-"b"))^(1/("a""b"))("x"^("b"-"c"))^(1/("b""c"))("x"^("c"-"a"))^(1/("c""a"))`
`="x"^(("a"-"b")/("a""b"))"x"^(("b"-"c")/("b""c"))"x"^(("c"-"a")/("c""a"))` .....`{("x"^"a")^"b"="x"^("a""b")}`
`="x"^(("a"-"b")/("a""b")+("b"-"c")/("b""c")+("c"-"a")/("c""a")`
`="x"^(("a""c"-"b""c"+"a""b"-"a""c"+"b""c"-"a""b")/("a""b"""c")`
c(a−b) + a(b−c) + b(c−a) = 0.
`0/(abc) = 0`
`="x"^0=1="R"."H"."S". ` .....`(∵"x"^0=1)`
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