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Category: Algebra

Let-f-x-be-a-quadratic-polynomial-with-integer-coefficients-such-that-f-0-and-f-1-are-odd-integers-Prove-that-the-equation-f-x-0-does-not-have-an-integer-solution-

Question Number 19245 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}\:{f}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{polynomial} \\ $$$$\mathrm{with}\:\mathrm{integer}\:\mathrm{coefficients}\:\mathrm{such}\:\mathrm{that}\:{f}\left(\mathrm{0}\right) \\ $$$$\mathrm{and}\:{f}\left(\mathrm{1}\right)\:\mathrm{are}\:\mathrm{odd}\:\mathrm{integers}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{f}\left({x}\right)\:=\:\mathrm{0}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\:\mathrm{an} \\ $$$$\mathrm{integer}\:\mathrm{solution}. \\ $$ Commented by RasheedSindhi last updated…

Question-19236

Question Number 19236 by chernoaguero@gmail.com last updated on 07/Aug/17 Answered by ,25>( last updated on 07/Aug/17 $${x}\:=\:\mathrm{2}\:\mathrm{since}\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{3}^{\mathrm{2}} \:=\:\mathrm{13}. \\ $$ Commented by chernoaguero@gmail.com last…

If-x-y-z-0-then-2-x-2-y-2-z-2-x-y-z-4-xy-4-yz-4-zx-1-

Question Number 150303 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}\:\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\left[\mathrm{0};\infty\right)\:\:\mathrm{then}: \\ $$$$\mathrm{2}^{\boldsymbol{\mathrm{x}}} +\mathrm{2}^{\boldsymbol{\mathrm{y}}} +\mathrm{2}^{\boldsymbol{\mathrm{z}}} +\mathrm{2}^{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}+\boldsymbol{\mathrm{z}}} \:\geqslant\:\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{xy}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{yz}}}} +\mathrm{4}^{\sqrt{\boldsymbol{\mathrm{zx}}}} +\mathrm{1} \\ $$ Answered by aleks041103 last…

Laplace-Metodu-solution-y-5y-6y-cos-t-y-0-0-and-y-0-1-

Question Number 150277 by mathdanisur last updated on 10/Aug/21 $$\mathrm{Laplace}\:\mathrm{Metodu}\:\left(\mathrm{solution}\right) \\ $$$$\mathrm{y}^{''} \:+\:\mathrm{5y}^{'} \:+\:\mathrm{6y}\:=\:\mathrm{cos}\left(\mathrm{t}\right) \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=\:\mathrm{1} \\ $$ Commented by amin96 last updated on…