if x= 1 / 2-√3 then find the value of x^2-4x+1​

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if x= 1 / 2-√3 then find the value of x^2-4x+1​

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Ella 1 week 2021-09-15T00:38:08+00:00 1 Answer 0 views 0

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    2021-09-15T00:40:03+00:00

    \rm\blue{GIVEN}

    • if x=\dfrac{1}{2-\sqrt{3}}

    \rm\blue{TO\:FIND}

    • \rm\red{x^{2}-4x+1}

    \rm\blue{HOW\:TO\:SOLVE}

    • We will Rationalise the value of x
    • We will take x as a Common and put the value of x.

    \implies\rm\red{x=\dfrac{1}{2-\sqrt{3}}}

    \implies\rm\red{x=\dfrac{1}{2-\sqrt{3}}×\dfrac{2+\sqrt{3}}{2+\sqrt{3}}}

    \implies\rm\red{x=\dfrac{2+\sqrt{3}}{1}}

    \implies\rm\red{x=\dfrac{2+\sqrt{3}}{1}}

    • Squaring the both sides.

    \implies\rm\red{(x)^2=(\dfrac{2+\sqrt{3}}{1}})^2}

    \implies\rm\red{x^2=4+4\sqrt{3}+3}

    \implies\rm\red{x^2=7+4\sqrt{3}}

    Again,

    \implies\bf\blue{x^2-4x+1}

    • Put the value of x and x² in the given equation

    \implies\bf\blue{7+4\sqrt{3}-(4(2+\sqrt{3})+1}

    \implies\bf\blue{7+{\cancel{4+\sqrt{3}}}-8-{\cancel{4+\sqrt{3}}}+1}

    \implies\bf\blue{8-8=0}

    Hence,The value of \rm\red{x^{2}-4x+1} is 0

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