 | Isaac Todhunter - 1861 - 330 páginas
...IX. OF THE DEPRESSION OF EQUATIONS. 121. In the present chapter we shall shew how the solution of an equation may be made to depend upon the solution of an equation of lower degree, in certain cases where known relations subsist among the roots ; this process is called... | |
 | Isaac Todhunter - 1875 - 344 páginas
...IX. OF THE DEPRESSION OF EQUATIONS. 121. In the present Chapter we shall shew how the solution .of an equation may be made to depend upon the solution of an equation of lower degree, in certain cases where known relations subsist among the roots; this process is called... | |
 | Isaac Todhunter - 1882 - 348 páginas
...IX. OF THE DEPRESSION OF EQUATIONS. 121. In the present Chapter we shall shew how the solution of an equation may be made to depend upon the solution of an equation of lower degree, in certain cases where known relations subsist among the roots; this process is called... | |
 | George Shoobridge Carr - 1886 - 1036 páginas
...Pr=Pn-r, or else pr=—pn-r467 A reciprocal equation of an even degree, with its last term positive, may be made to depend upon the solution of an equation of half the same degree. 468 EXAMPLE : 4гч - 24z5 + 57ж* - 73a*1 + 57ж2 - 24» + 4 = О is a reciprocal... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - 1891 - 606 páginas
...seen that the solution in positive integers of the equation ax2 + 2hxy + by1 + 2gx + 2fy + c = 0 can be made to depend upon the solution of an equation of the form x1 ± Ny1 = ± a, where N and a are positive integers. The equation a? + Ny* = — a has no real roots,... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - 1893 - 434 páginas
...Application of Trigonometry to the Theory of Equations. 326. In the Theory of Equations it is shewn that the solution of any cubic equation may be made to depend on the solution of a cubic equation of the form x? + ax-\-bs=0. In certain cases the solution is very... | |
 | Leonard Eugene Dickson - 1902 - 242 páginas
...special equations were solved by means of equations of lower degree, so the solution of any reciprocal equation may be made to depend upon the solution of an equation of lower degree. If the given equation is the equation obtained by writing — for y aud multiplying by... | |
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Thus 3 and — 4 are roots ; and since x = -~ , we have -. and - 2 •"* ~ as roots of the original equation. IX. OF THE DEPRESSION OF EQUATIONS. 121. In the present Chapter we shall shew how the solution .of an equation may be made to depend upon the... 