X^-2+4x^-1+3=0 solve by making appropriate substitution

Question

X^-2+4x^-1+3=0 solve by making appropriate substitution

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Vivian 1 week 2021-09-15T23:00:14+00:00 1 Answer 0

Answers ( )

  1. ANSWER

    x =  - 1 \: or \: x =  -  \frac{1}{ 3}

    EXPLANATION

    The given equation is:

     {x}^{ - 2}  + 4 {x}^{ - 1}  + 3 = 0

    Recall that:

     {a}^{ - m}  =  \frac{1}{ {a}^{m} }

     \frac{1}{ {x}^{2} }  +  \frac{4}{x}  + 3 = 0

    Or

     {( \frac{1}{x} )}^{2}  + 4( \frac{1}{x} ) + 3 = 0

    Let

    u =  \frac{1}{x}

    Our equation then becomes:

     {u}^{2}  + 4u + 3 = 0

    The factors of 3 that add up to 4 are:

     {u}^{2}  + 3u + u + 3

    u(u + 3) + 1(u + 3) = 0

    (u + 1)(u + 3) = 0

    u + 1 = 0 \: or \: u + 3 = 0

    u =  - 1 \: or \: u =  - 3

    This implies that:

     \frac{1}{x}  =  - 1 \: or \:  \frac{1}{x}  =  - 3

    x =  - 1 \: or \: x =  -  \frac{1}{ 3}

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