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Category: Arithmetic

If-a-b-are-real-numbers-amp-4cos-2-4a-2-9b-2-5-a-3b-then-the-value-of-a-b-will-be-a-7-6-b-5-4-c-11-6-d-17-12-

Question Number 194552 by BaliramKumar last updated on 09/Jul/23 $$\mathrm{If}\:{a},\:{b}\:\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}\:\&\:\mathrm{4cos}^{\mathrm{2}} \theta\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} +\mathrm{9}{b}^{\mathrm{2}} +\mathrm{5}}{{a}+\mathrm{3}{b}},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left({a}+{b}\right)\:\mathrm{will}\:\mathrm{be}: \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{7}}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{5}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\frac{\mathrm{11}}{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{17}}{\mathrm{12}} \\ $$ Commented by Frix last updated on…

Let-N-be-a-natural-number-where-N-100-If-HCF-N-100-1-then-find-the-sum-of-all-the-values-of-N-a-400-b-1000-c-2000-d-4000-

Question Number 194528 by BaliramKumar last updated on 09/Jul/23 $$\bigstar\:\mathrm{Let}\:\mathrm{N}\:\mathrm{be}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{where}\:\mathrm{N}\leq\mathrm{100}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{If}\:\mathrm{HCF}\left(\mathrm{N},\:\mathrm{100}\right)\:=\:\mathrm{1}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{N}\:? \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{a}\right)\:\mathrm{400}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{1000}\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2000}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{4000} \\ $$ Answered by mahdipoor last updated on 09/Jul/23…

How-many-sets-of-two-factors-of-720-are-coprime-to-each-other-A-63-B-64-C-65-D-67-

Question Number 194475 by BaliramKumar last updated on 08/Jul/23 $$\mathrm{How}\:\mathrm{many}\:\mathrm{sets}\:\mathrm{of}\:\mathrm{two}\:\mathrm{factors}\:\mathrm{of}\:\mathrm{720}\:\mathrm{are}\: \\ $$$$\mathrm{coprime}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$\left(\mathrm{A}\right)\:\mathrm{63}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{64}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{65}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{67} \\ $$$$ \\ $$ Commented by MM42 last updated on 08/Jul/23…

If-a-b-c-gt-0-such-that-a-b-c-3-prove-that-1-1-ab-1-1-ac-1-1-bc-9-2-a-b-c-

Question Number 194448 by York12 last updated on 07/Jul/23 $${If}\:{a}\:,\:{b}\:,\:{c}\:>\mathrm{0}\:,\:{such}\:{that}\:{a}+{b}+{c}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{ab}}+\frac{\mathrm{1}}{\mathrm{1}+{ac}}+\frac{\mathrm{1}}{\mathrm{1}+{bc}}\geqslant\frac{\mathrm{9}}{\mathrm{2}\left(\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

If-a-b-c-gt-0-such-that-a-b-c-3-prove-that-1-1-ab-1-1-ac-1-1-bc-9-2-a-b-c-

Question Number 194421 by York12 last updated on 06/Jul/23 $$ \\ $$$${If}\:{a}\:,\:{b}\:,\:{c}\:>\mathrm{0}\:,\:{such}\:{that}\:{a}+{b}+{c}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+{ab}}+\frac{\mathrm{1}}{\mathrm{1}+{ac}}+\frac{\mathrm{1}}{\mathrm{1}+{bc}}\geqslant\frac{\mathrm{9}}{\mathrm{2}\left(\sqrt{{a}}+\sqrt{{b}}+\sqrt{{c}}\right)} \\ $$ Commented by York12 last updated on 07/Jul/23…