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Category: Algebra

Given-a-3-1-3-1-3-Find-the-value-of-3a-3-9a-1-

Question Number 134763 by bramlexs22 last updated on 07/Mar/21 $$\mathrm{Given}\:{a}=\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}{a}^{\mathrm{3}} −\mathrm{9}{a}+\mathrm{1}. \\ $$ Answered by EDWIN88 last updated on 07/Mar/21 $$=\:\frac{\mathrm{3}\sqrt{\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{9}}}{\mathrm{3}}\:+\frac{\mathrm{2}\sqrt{\mathrm{3}}\:\sqrt[{\mathrm{6}}]{\mathrm{243}}}{\mathrm{9}}−\frac{\mathrm{26}\:\sqrt{\mathrm{3}}}{\mathrm{9}}\:+\frac{\mathrm{2}\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:\sqrt[{\mathrm{6}}]{\mathrm{243}}}{\mathrm{3}}−\frac{\mathrm{26}\:\sqrt[{\mathrm{3}}]{\mathrm{3}}}{\mathrm{3}}+\mathrm{4} \\ $$…

r-1-n-1-r2-r-

Question Number 3682 by Yozzii last updated on 19/Dec/15 $$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{r}\mathrm{2}^{{r}} }=? \\ $$ Commented by RasheedSindhi last updated on 19/Dec/15 $$\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{r}\mathrm{2}^{{r}}…

Question-69201

Question Number 69201 by ahmadshah last updated on 21/Sep/19 Answered by Kunal12588 last updated on 21/Sep/19 $${f}\left({x}\right)=\frac{{x}−\mathrm{5}}{{x}^{\mathrm{2}} −\mathrm{25}}=\frac{{x}−\mathrm{5}}{\left({x}−\mathrm{5}\right)\left({x}+\mathrm{5}\right)} \\ $$$$\Rightarrow\left({x}−\mathrm{5}\right)\left({x}+\mathrm{5}\right)\neq\mathrm{0} \\ $$$$\Rightarrow{x}\neq\mathrm{5},−\mathrm{5} \\ $$$$\therefore{x}\in\mathbb{R}−\left\{−\mathrm{5},\mathrm{5}\right\} \\…

If-a-n-is-sum-of-the-all-primitive-n-th-root-of-unity-Does-n-1-a-n-converge-An-n-th-root-of-unity-say-z-is-primitive-if-it-is-not-k-th-root-of-unity-where-k-lt-n-or-z-n-1-and-z

Question Number 3650 by prakash jain last updated on 18/Dec/15 $$\mathrm{If}\:{a}_{{n}} \:\mathrm{is}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{all}\:\mathrm{primitive}\:{n}^{{th}} \:\mathrm{root}\:\mathrm{of} \\ $$$$\mathrm{unity}. \\ $$$$\mathrm{Does}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} \:\mathrm{converge}? \\ $$$$\mathrm{An}\:{n}^{{th}} \:\mathrm{root}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{say}\:{z},\:\mathrm{is}\:\mathrm{primitive}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{not} \\ $$$${k}^{{th}}…

If-the-G-M-between-two-numbers-a-b-is-G-and-the-two-A-M-s-between-them-are-p-and-q-then-prove-that-G-2-2p-q-2q-p-

Question Number 3617 by Rasheed Soomro last updated on 16/Dec/15 $${If}\:\:{the}\:{G}.{M}.\:{between}\:{two}\:{numbers}\: \\ $$$${a}\:,\:{b}\:\:\:{is}\:\:{G}\:{and}\:{the}\:{two}\:{A}.{M}.'{s}\:{between} \\ $$$${them}\:{are}\:{p}\:\:{and}\:\:{q}\:,\:{then}\:{prove}\:{that} \\ $$$${G}^{\mathrm{2}} =\left(\mathrm{2}{p}−{q}\right)\left(\mathrm{2}{q}−{p}\right). \\ $$ Commented by Yozzii last updated…