Category: Algebra

Question Number 195124 by Shlock last updated on 25/Jul/23 Answered by witcher3 last updated on 25/Jul/23 $$\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}⩽\sqrt{(\mathrm{x}+1)(\mathrm{y}+1)}$$$$\iff \mathrm{x}+\mathrm{y}+2\sqrt{\mathrm{xy}}⩽\mathrm{xy}+\mathrm{x}+\mathrm{y}+1\iff \mathrm{xy}+1⩾2\sqrt{\mathrm{xy}},\mathrm{AM}-\mathrm{GM}$$$$\Rightarrow \mathrm{\forall }(\mathrm{x},\mathrm{y})\in {\mathbb{R}}_{+}\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}⩽\sqrt{(\mathrm{x}+1)(\mathrm{y}+1)}$$$$\Rightarrow\forall\left(\mathrm{a},\mathrm{b}\right)\in\left[\mathrm{1},\infty\left[^{\mathrm{2}} \right.\right.…

Question Number 195122 by Rupesh123 last updated on 25/Jul/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 195116 by SajaRashki last updated on 24/Jul/23 $$hi.pleaserepresntation\sqrt[3]{2}on{number}^{\prime }saxis$$$$withrulerandcompassandpen.$$$$thankyou$$ Commented by Frix last updated on 25/Jul/23 $$\mathrm{Impossible}. \…

Question Number 195107 by Rupesh123 last updated on 24/Jul/23 Answered by JDamian last updated on 24/Jul/23 $$5+15+25+\cdot \cdot \cdot +975+985+995=$$$$=\frac{100}{2}(5+995)=50000$$ Terms of Service Privacy…

Question Number 195027 by York12 last updated on 22/Jul/23 $$a_3{x}^3-x^2+a_{1}x-7=0isacubicpolynomialinx$$$$whoseRootsare\alpha ,\beta ,\gamma positiverealnumbers$$$$satisfying$$$$\frac{\mathrm{225}\alpha^{\mathrm{2}} }{\alpha^{\mathrm{2}} +\mathrm{7}}=\frac{\mathrm{144}\beta^{\mathrm{2}} }{\beta^{\mathrm{2}} +\mathrm{7}}=\frac{\mathrm{100}\gamma^{\mathrm{2}} }{\gamma^{\mathrm{2}}…