text: what the heck is this? the sum of two numbers is fourteen. the sum of the squares of the two numbers is one hundred thirty. find the two numbers.   3 and 11     4 and 10      5 and 9      2 and 12 x + y = 14 ...so ...x = 14 - y  x^2 +y^2 = 130 ...plugging in x from above...  (14-y)^2 + y^2 = 130   ...multiply out your products...  196 -28y +y^2 + y^2 = 130  ...combining your y^2  2y^2 -28y +196 -130 = 0  ....moving over the 130  2y^2 -28y + 66 = 0  ...dividing equation by 2 y^2 -14y + 33 = 0  ...performing foil method and finding roots...  y = (y-11)(y-3) = 0 ...y can be 11 or 3  if y is 11, then plugging back into x = 14 - y...x is 3 if y is 3, then plugging back into x = 14 - y...x is 11  so your two number can be 11 and 3   actually, if you don't want to do the algebra... 4x4 + 10x10 = 116 not 130 5x5 + 9x9 = 106 not 130  and 2x2 + 12x12 = 148 not 130  so 3 and 11 can be your only solutions