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Category: Algebra

Given-a-b-5ab-b-c-7bc-c-a-6ac-where-a-b-c-0-Find-abc-

Question Number 134912 by bramlexs22 last updated on 08/Mar/21 $$\mathrm{Given}\:\begin{cases}{\mathrm{a}+\mathrm{b}=\mathrm{5ab}}\\{\mathrm{b}+\mathrm{c}=\mathrm{7bc}}\\{\mathrm{c}+\mathrm{a}=\mathrm{6ac}}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\neq\:\mathrm{0}. \\ $$$$\mathrm{Find}\:\mathrm{abc} \\ $$ Answered by Ñï= last updated on 08/Mar/21 $$\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}=\mathrm{5}\Leftrightarrow{A}+{B}=\mathrm{5} \\…

Show-that-a-b-R-a-b-1-3-b-a-1-3-2-a-b-1-a-1-b-1-3-

Question Number 3832 by Yozzii last updated on 21/Dec/15 $${Show}\:{that},\:\forall{a},{b}\in\mathbb{R}^{+} , \\ $$$$\:\left(\frac{{a}}{{b}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{{b}}{{a}}\right)^{\mathrm{1}/\mathrm{3}} \leqslant\left\{\mathrm{2}\left({a}+{b}\right)\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\right\}^{\mathrm{1}/\mathrm{3}} . \\ $$$$ \\ $$ Commented by RasheedSindhi last updated…

n-0-2n-1-2-2n-1-

Question Number 3807 by Rasheed Soomro last updated on 21/Dec/15 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}^{\mathrm{2}{n}+\mathrm{1}} }=? \\ $$ Answered by Yozzii last updated on 21/Dec/15 $${s}=\underset{{n}=\mathrm{0}} {\overset{\infty}…

Let-a-i-1-i-10-be-the-roots-of-the-equation-m-1-10-mx-m-0-Prove-that-100-i-1-10-a-i-2-1-61-An-algebra-question-as-seen-on-Brilliant-

Question Number 3775 by Yozzii last updated on 20/Dec/15 $${Let}\:{a}_{{i}} \:\left(\mathrm{1}\leqslant{i}\leqslant\mathrm{10}\right)\:{be}\:{the}\:{roots}\:{of}\:{the} \\ $$$${equation}\:\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}{mx}^{{m}} =\mathrm{0}.\:{Prove}\:{that} \\ $$$$\mathrm{100}\underset{{i}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}\left({a}_{{i}} ^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{61}. \\ $$$$\left({An}\:{algebra}\:{question}\:{as}\:{seen}\:{on}\:{Brilliant}.\right) \\…

Question-69297

Question Number 69297 by ajfour last updated on 22/Sep/19 Commented by ajfour last updated on 22/Sep/19 $${If}\:{the}\:{graph}\:{is}\:{a}\:{cubic} \\ $$$$\:\:\:\:{y}={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${find}\:{point}\:{of}\:{intersection}\:{of} \\ $$$${the}\:{red}\:{and}\:{blue}\:{lines}.…