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Thread: Manhattan Algebra Strategy Volume Hard exercise problem

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    Manhattan Algebra Strategy Volume Hard exercise problem

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    The equation given is

    a= 5b^2+ 10b + 7

    Which is greater- a or b?

    They say to do it by completing the square but I simply do not understand their solution! Please help me out with the easiest solution.

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    Re: Manhattan Algebra Strategy Volume Hard exercise problem

    Hi Ramlah ,

    Did you get the solution ?

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    Re: Manhattan Algebra Strategy Volume Hard exercise problem

    Hey so in here, there's really two cases:

    We see that a depends on b.

    So if b>0, then obviously a > b.
    If b<0, we see that the quadratic term 5b^2 is always positive and grows way quicker than the linear term 10b, and the final sum is helped by +7. You can test this out with the largest possible value for b, b=-1 assuming and b are integers. So a >0 and thus a>b here too.

    So in the final answer, we see that a > b for both situations. So choice that says a>b is correct

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