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Category: Algebra

If-a-b-c-1-a-2-b-2-c-2-2-a-3-b-3-c-3-3-then-a-5-b-5-c-5-

Question Number 57791 by Tawa1 last updated on 12/Apr/19 $$\:\mathrm{If}\:\:\:\:\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\:=\:\:\mathrm{1}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{c}^{\mathrm{3}} \:\:=\:\:\mathrm{3}\:\: \\ $$$$\mathrm{then}\:\:\:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}\:\:} =\:\:?…

Prove-that-n-2-3n-2-is-divisible-by-2-for-any-n-Z-

Question Number 188776 by depressiveshrek last updated on 06/Mar/23 $$\mathrm{Prove}\:\mathrm{that}\:{n}^{\mathrm{2}} +\mathrm{3}{n}+\mathrm{2}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{2} \\ $$$$\mathrm{for}\:\mathrm{any}\:{n}\in\mathbb{Z} \\ $$ Commented by Frix last updated on 08/Mar/23 $$\mathrm{2}\mid{n}\:\Rightarrow\:\mathrm{2}\mid{n}^{\mathrm{2}} \wedge\mathrm{2}\mid\mathrm{3}{n} \\…

Question-188774

Question Number 188774 by Shrinava last updated on 06/Mar/23 Answered by aleks041103 last updated on 09/Mar/23 $${Diagonlize}\:{A},\:{i}.{e}.\:{A}={P}^{−\mathrm{1}} {DP},\:{where}\:{D} \\ $$$${is}\:{diagonal}. \\ $$$${Now}\:{you}\:{can}\:{chose}\:{as}\:{many}\:{as}\:{you}\:{want} \\ $$$${two}\:{more}\:{diagonal}\:{matrices}\:{D}_{\mathrm{1}} \:{and}\:{D}_{\mathrm{2}}…

Find-the-sum-of-the-cubes-of-first-n-even-number-and-first-n-odd-number-

Question Number 57635 by Tawa1 last updated on 09/Apr/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{even}\:\mathrm{number},\:\:\mathrm{and} \\ $$$$\mathrm{first}\:\mathrm{n}\:\mathrm{odd}\:\mathrm{number}. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 09/Apr/19 $${As}\:{per}\:{higher}\:{algebra}\:{Bernard}\:{and}\:{child} \\ $$$${we}\:{can}\:{find}\: \\…