Category: Algebra

Question Number 119540 by AlbinEA last updated on 25/Oct/20 Answered by Bird last updated on 25/Oct/20 $$kitchenthorem\dots .$$ Terms of Service Privacy Policy Contact:…

Question Number 119538 by kailla last updated on 25/Oct/20 Commented by benjo_mathlover last updated on 25/Oct/20 $$badimage$$ Answered by joki last updated on…

Question Number 119490 by Ar Brandon last updated on 25/Oct/20 $$\mathrm{Let}a<\mathrm{c}<\mathrm{b}\mathrm{such}\mathrm{that}\mathrm{c}-a=\mathrm{b}-\mathrm{c}.\mathrm{If}f:\mathbb{R}\to \mathbb{R}\mathrm{is}\mathrm{a}$$$$\mathrm{function}\mathrm{satisfying}\mathrm{the}\mathrm{relation}$$$$f(\mathrm{x}+a)+f(\mathrm{x}+\mathrm{b})=f(\mathrm{x}+\mathrm{c})\mathrm{for}\mathrm{all}\mathrm{x}\in \mathbb{R}$$$$\mathrm{then}\mathrm{a}\mathrm{period}\mathrm{of}f\mathrm{is}$$$$\left(\mathrm{A}\right)(\mathrm{b}-a)\left(\mathrm{B}\right)2(\mathrm{b}-a)$$$$\left(\mathrm{C}\right)3(\mathrm{b}-a)\left(\mathrm{D}\right)4(\mathrm{b}-a)$$ Terms of…

Question Number 119483 by Ar Brandon last updated on 24/Oct/20 $$\mathrm{Let}a>0\mathrm{and}f:\mathbb{R}\to \mathbb{R}\mathrm{a}\mathrm{function}\mathrm{satisfying}$$$$f(\mathrm{x}+a)=1+{[2-3f\left(\mathrm{x}\right)+3f{\left(\mathrm{x}\right)}^2-f{\left(\mathrm{x}\right)}^3]}^{1/3}$$$$\mathrm{for}\mathrm{all}\mathrm{x}\in \mathbb{R}.\mathrm{Then}\mathrm{a}\mathrm{period}\mathrm{of}f\left(\mathrm{x}\right)\mathrm{is}ka\mathrm{where}k\mathrm{is}$$$$\mathrm{a}\mathrm{positive}\mathrm{integer}\mathrm{whose}\mathrm{value}\mathrm{is}$$$$\left(\mathrm{A}\right)1\left(\mathrm{B}\right)2\left(\mathrm{C}\right)3\left(\mathrm{D}\right)4$$ Answered by…

Question Number 184980 by Shrinava last updated on 15/Jan/23 $$\sqrt{7}+\sqrt{6}=\mathrm{a}$$$$\sqrt{7}-\sqrt{6}=?$$ Answered by SEKRET last updated on 15/Jan/23 $$\times \{\begin{array}{l}\sqrt{7}+\sqrt{6}=\mathbf{a}\\ \sqrt{7}-\sqrt{6}=\mathbf{x}\end{array}$$$$\:\:\:\boldsymbol{\mathrm{ax}}=\:\mathrm{1} \…