...it will only be necessary to make 1 + xa square, in order that the whole expression may be a square. PROBLEM III. To find such values of x as will render rational the expression •S/<MM + bx3 + ex2 + dx + e. In this problem there are three cases in which a direct solution can...

...form ; the principal methods of effecting which are comprehended in the following problems. PROBLEM I. To find such values of x as will render rational the expression + bx + c. Before we can give any direct investigation of this problem, it will be necessary to consider...

...3y4-f1V=fMF2/4-PrV\V. or %-f!4 = f Шу-ртУ^ ; whence у = -VoW^ and> consequently, Problem IV. To find such values of x as will render rational the expression ty(ai?-\-b3?-\-cx-\-d.) In this problem there are likewise only three cases in which a direct solution...

...additions," " Barlow'i Theory of Numbers," and "Legendre Theorie des Nombre"" ART. 15. PROBLEM 1. — To find such values of x as will render rational the expression The solution of this problem assumes different forms, depending on the values of a, b, and c. Акт....