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Category: Algebra

found-something-interesting-it-was-published-by-Tschirnhaus-in-1683-we-can-reduce-x-3-ax-2-bx-c-0-1-to-y-3-py-q-0-2-and-further-to-z-3-t-1-is-the-well-known-linear-substitution-y-x-a-3-

Question Number 54775 by MJS last updated on 10/Feb/19 $$\mathrm{found}\:\mathrm{something}\:\mathrm{interesting},\:\mathrm{it}\:\mathrm{was}\:\mathrm{published} \\ $$$$\mathrm{by}\:\mathrm{Tschirnhaus}\:\mathrm{in}\:\mathrm{1683} \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{reduce} \\ $$$${x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{to} \\ $$$${y}^{\mathrm{3}} +{py}+{q}=\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{and}\:\mathrm{further}\:\mathrm{to}…

Question-120229

Question Number 120229 by Algoritm last updated on 30/Oct/20 Answered by benjo_mathlover last updated on 30/Oct/20 $$\sqrt{\mathrm{36}\left({x}^{\mathrm{2}} +\mathrm{1}\right)−{x}}\:+\sqrt{{x}^{\mathrm{2}} +\mathrm{36}\left({x}+\mathrm{1}\right)}\:=\:{x}^{\mathrm{2}} \\ $$$$\sqrt{\mathrm{36}\left(\left[{x}+\mathrm{1}\right]^{\mathrm{2}} −\mathrm{2}{x}\right)−{x}}\:+\sqrt{{x}^{\mathrm{2}} +\mathrm{36}\left({x}+\mathrm{1}\right)}\:=\:{x}^{\mathrm{2}} \\ $$$$\sqrt{\mathrm{36}\left({x}+\mathrm{1}\right)^{\mathrm{2}}…