Solve using inequalities x^-8x+7/4x^2-4x+1<0

Question

Solve using inequalities x^-8x+7/4x^2-4x+1<0

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Lyla 7 days 2021-09-12T16:37:49+00:00 1 Answer 0 views 0

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    2021-09-12T16:39:09+00:00

    Given,

    \longrightarrow\dfrac{x^2-8x+7}{4x^2-4x+1}<0

    Factorising numerator and denominator each,

    \longrightarrow\dfrac{x^2-x-7x+7}{4x^2-2x-2x+1}<0

    \longrightarrow\dfrac{x(x-1)-7(x-1)}{2x(2x-1)-(2x-1)}<0

    \longrightarrow\dfrac{(x-1)(x-7)}{(2x-1)(2x-1)}<0

    \longrightarrow\dfrac{(x-1)(x-7)}{(2x-1)^2}<0

    Here the denominator (2x-1)^2 is always positive since it’s something squared.

    So the numerator should be negative for satisfying the inequality.

    Therefore,

    \longrightarrow(x-1)(x-7)<0

    Solution to this inequality is,

    \longrightarrow\underline{\underline{x\in(1,\ 7)}}

    Thus solved!

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