show that x^a+b×x^b+c×x^c+a/(x^a×x^b×x^c) = 1​

Question

show that x^a+b×x^b+c×x^c+a/(x^a×x^b×x^c) = 1​

in progress 0
Autumn 4 weeks 2021-08-23T05:31:34+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-23T05:32:45+00:00

    Answer:

    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

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )