Aptitude topic. Question on averages

A two-digit number exceeds the sum of its squares by 19 and doubles the product of its digit by 44.find the number

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  • let xand y be the number represented by 10x+y 

    10x + y = x^2 + y^2 + 19
    10x + y = 2xy + 44
    10x + y = 2xy + 44
    y - 2xy = 44 - 10x

    y(1 - 2x) = 44 - 10x
    y = (44 - 10x)/(1 - 2x)
    Now, plug:
    10x + y = x^2 + y^2 + 19
    10x + (44 - 10x)/(1 - 2x) = x^2 + [(44 - 10x)/(1 - 2x)]^2 + 19
    Long story short: (7,2) and (3.5,-1.5) 
    the decimals are excluded because they don't result with two digits
    10x + y
    10(7) + 2
    72
     
    0
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