Question 536342
The difference of 2 numbers is 180. Square of smaller number is 8 times the larger number. find the numbers?


Let the larger and smaller numbers be L and S, respectively

Then: L – S = 180 ------ L = 180 + S ------ eq (i)
{{{S^2 = 8L}}} ----- {{{S^2 - 8L = 0}}} ------- eq (ii)


{{{S^2 - 8(180 + S) = 0}}} ------ Substituting 180 + S for L in eq (ii)


{{{S^2 - 1440 - 8S = 0}}}


{{{S^2 - 8S - 1440 = 0}}}


Solving using the quadratic formula, we find that S, or smaller number = {{{highlight_green(42.1576)}}}, or {{{highlight_green(- 34.1576)}}}


If smaller number = {{{42.1576}}}, then larger number = {{{highlight_green(222.1576)}}}


However, if smaller number = {{{- 34.1576}}}, then larger number = {{{highlight_green(145.8424)}}}


I'm sure you can do the check!!


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