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A natural number whose square diminished …

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A natural number whose square diminished by 84.The larger number is 5 less twice of the smaller number.Find the two number.

    • Posted by Asish Kumar Sahani 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 5 months ago

    Let the required number be x.
    Then, square of a number will be x2.
    According to given information, we have
    {tex}x^2 - 84 = 3(x + 8){/tex}
    {tex} \Rightarrow {/tex} {tex}x^2 - 84 = 3x + 24{/tex}
    {tex} \Rightarrow {/tex} {tex}x^2 - 3x - 108 = 0{/tex}
    {tex} \Rightarrow {/tex} {tex}x^2 - 12x + 9x - 108 = 0{/tex}
    {tex} \Rightarrow {/tex} {tex}x(x - 12) + 9(x - 12) = 0{/tex}
    {tex} \Rightarrow {/tex} {tex}(x - 12)(x + 9) = 0{/tex}
    {tex} \Rightarrow {/tex} x - 12 = 0 or x + 9 = 0
    {tex} \Rightarrow {/tex} x = 12 or x = -9
    Since x is a natural number, x {tex}\ne{/tex} -9.
    {tex} \Rightarrow {/tex} x = 12
    Hence, required number is 12.

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