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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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Answer» Answer: Prove that (x^a/x^b) ^1/AB ( x^b /x^c) ^1/bc (x^c/x^a) ^1/ca= 1 Given: (xa/xb)^1/ab( xb /XC)^1/bc(xc/xa)1/ca We need to prove the gives equation is unity that si 1 LHS=(xa/xb)^1/ab( xb /xc)^1/bc(xc/xa)1/ca Using laws of EXPONENTS = (xa/xb)1/ab( xb /xc)1/bc(xc/xa)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[c(a-b)/abc + a(b-c)/abc + b(c-a)/abc ] = x { [c(a-b)+ a(b-c) + b(c-a) ]/abc } = x ( ac – bc + ab – ac + bc – ab ] /abc = x 0/abc = X0 = 1 = RHS Hence proved |
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