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godwin_ibrahim
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Tyro
Asked: 2020-11-14T10:32:34+00:00 In:

What is the base number x given 641_{x}+156_{x}=807_{x}

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What is the base number x given 641_{x}+156_{x}=807_{x}

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  2. Sengemegz
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    641_{x}+156_{x}=807_{x}
    convert each of them to base 10
    6\times x^{2}+4\times x^{1}+1\times x^{0}+1\times x^{2}+5\times x^{1}+6\times x^{0}=8\times x^{2}+0\times x^{1}+7\times x^{0}
    \Rightarrow 6x^{2}+4x+1+x^{2}+5x+6=8x^{2}+0+7
    \Rightarrow 7x^{2}+9x+7=8x^{2}+7
    collect like terms
    7x^{2}+9x+7-8x^{2}-7=0
    \Rightarrow -x^{2}+9x=0
    \Rightarrow x^{2}-9x=0
    factorising the equation
    x(x-9)=0
    \Rightarrow x=0 or x-9=0
    \Rightarrow x=0 or x=9

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