Category: Algebra

Question Number 151241 by bagjagugum123 last updated on 19/Aug/21 Answered by hknkrc46 last updated on 19/Aug/21 $$\left(2\right)\mid 2\mathit{x}-3\mid <\mid \mathit{x}-1\mid$$$$\Rightarrow {(2\mathit{x}-3)}^2<{(\mathit{x}-1)}^2$$$$\:\:\:\:\:\:\:\Rightarrow\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{12}\boldsymbol{{x}}\:+\:\mathrm{9}\:<\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{2}\boldsymbol{{x}}\:+\:\mathrm{1} \…

Question Number 151224 by mathdanisur last updated on 19/Aug/21 Answered by Rasheed.Sindhi last updated on 19/Aug/21 $$Let{there}^{\prime }rexboysandygirls$$$$minimumnumberofsliceseaten$$$$=4x+2y$$$$\left(4slices/boy\mathrm{\&}2slices/girl\right)$$$$\mathrm{4}{x}+\mathrm{2}{y}>\mathrm{16}\:\:\left(\mathrm{2}\:{cakes},\:\mathrm{8}\:{slices}\:{per}\:{each}\:{cake}\right)…

Question Number 151212 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}{\mathrm{a}}_1,{\mathrm{a}}_2,\dots {\mathrm{a}}_{\mathbf{n}}>1\mathrm{then}:$$$$\sqrt{\frac{\left(\mathrm{a}_{\mathrm{1}} -\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} -\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} -\mathrm{1}\right)}{\left(\mathrm{a}_{\mathrm{1}} +\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} +\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} +\mathrm{1}\right)}}\:\leqslant\:\frac{\mathrm{a}_{\mathrm{1}} \mathrm{a}_{\mathrm{2}} …\mathrm{a}_{\boldsymbol{\mathrm{n}}} }{\mathrm{2}^{\boldsymbol{\mathrm{n}}} }…

Question Number 151215 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\mathrm{x};\mathrm{y};\mathrm{z}>0;\mathrm{x}+\mathrm{y}+\mathrm{z}=1\mathrm{and}\lambda ⩾\frac{1}{6}\mathrm{then}:$$$$\mathit{\lambda }\mathrm{\Sigma }\frac{\mathrm{y}+\mathrm{z}}{\mathrm{x}}+3\mathrm{\Sigma }\mathrm{yz}⩾6\mathit{\lambda }+1$$ Answered by dumitrel last updated on 19/Aug/21 $$p=1$$$${p}^{\mathrm{2}} \geqslant\mathrm{3}{q}\Rightarrow{q}\leqslant\frac{\mathrm{1}}{\mathrm{3}}\leqslant\mathrm{2}\lambda…

Question Number 151211 by EDWIN88 last updated on 19/Aug/21 $$Findthecoefficientof{x}^9$$$$fromexpression$$$$(1+x)(1+2x^2)(1+3x^3)(1+4x^4)(1+5x^5)\dots (1+10x^{10})$$ Answered by Olaf_Thorendsen…