Category: Algebra

Question Number 151332 by mathdanisur last updated on 20/Aug/21 $$\mathrm{which}\mathrm{is}\mathrm{larger}?$$$$2^{\sqrt{10}}\mathrm{or}{3}^2$$ Commented by liberty last updated on 20/Aug/21 $$3^2$$…

Question Number 151322 by mathdanisur last updated on 20/Aug/21 $$\mathrm{Determine}\mathrm{all}\mathrm{pairs}(\mathrm{x};\mathrm{y})\mathrm{of}\mathrm{integers}$$$$\mathrm{which}\mathrm{satisfy}:$$$${\mathrm{x}}^3-3\mathrm{x}+\mathrm{y}=0$$ Commented by mathdanisur last updated on 20/Aug/21 $$\mathrm{with}\:\boldsymbol{\mathrm{x}}\:\mathrm{real},\:\boldsymbol{\mathrm{y}}\:\mathrm{integer}…

Question Number 151317 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}\mathbf{x}=\sqrt[3]{\sqrt{7}-\sqrt{6}}+\sqrt[3]{\sqrt{7}+\sqrt{6}}$$$$\mathrm{find}\mathrm{E}\left(\mathrm{x}\right)={\mathrm{x}}^6-{6\mathrm{x}}^4+{9\mathrm{x}}^2=?$$ Answered by iloveisrael last updated on 20/Aug/21 $$\:{we}\:{have}\:{x}−\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}−\sqrt{\mathrm{6}}}−\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{7}}+\sqrt{\mathrm{6}}}\:=\:\mathrm{0}…

Question Number 151315 by mathdanisur last updated on 20/Aug/21 $$\mathrm{if}{\mathrm{x}}^2+{\mathrm{y}}^2={16}^2;{\mathrm{y}}^2+{\mathrm{z}}^2={24}^2$$$${\mathrm{z}}^2+{\mathrm{t}}^2={42}^2\mathrm{and}{\mathrm{t}}^2+{\mathrm{x}}^2={38}^2$$$$\mathrm{find}\:\:\mathrm{max}\left[\left(\mathrm{x}+\mathrm{z}\right)\left(\mathrm{y}+\mathrm{t}\right)\right]=? \…

Question Number 151307 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\mathrm{x}\sqrt{\mathrm{x}}-26\sqrt{\mathrm{x}}=5$$$$\mathrm{find}\mathrm{x}-5\sqrt{\mathrm{x}}=?$$ Answered by MJS_new last updated on 20/Aug/21 $$x\sqrt{x}-26\sqrt{x}-5=0$$$$\left(\sqrt{{x}}+\mathrm{5}\right)\left({x}−\mathrm{5}\sqrt{{x}}−\mathrm{1}\right)=\mathrm{0} \…