Category: Algebra

Question Number 98914 by shaxzod last updated on 17/Jun/20 $$2x+3y=5$$$$\text{Missing left or extra right}$$ Commented by john santu last updated on 17/Jun/20…

Question Number 164434 by mathlove last updated on 17/Jan/22 Answered by TheSupreme last updated on 17/Jan/22 $$2f\left(sin\left(x\right)\right)-f\left(cos\left(x\right)\right)=3x$$$$2f\left(cos\left(x\right)\right)-f\left(sin\left(x\right)\right)=3(\frac{\pi }{2}-x)$$$$3f\left(sin\left(x\right)\right)=6x-3(\frac{\pi }{2}-x)$$$$f\left(sin\left(x\right)\right)=9x-\frac{3}{2}\pi$$$${f}\left({t}\right)=\mathrm{9}{arcsin}\left({x}\right)−\frac{\mathrm{3}}{\mathrm{2}}\pi+\mathrm{2}{k}\pi…

Question Number 164425 by Zaynal last updated on 17/Jan/22 $$\mathrm{What}{\mathrm{it}}^{\prime }\mathrm{s}??$$$$5\times 55\times 555\times 5555\times 55555\dots \dots \dots \dots .\mathrm{\infty }=$$ Answered by alephzero last updated on 17/Jan/22 $$\mathrm{Let}\:{a}_{{n}} \:=\:\underset{{n}-\mathrm{times}} {\underbrace{\mathrm{5555}…\mathrm{5555}}} \…

Question Number 164416 by HongKing last updated on 16/Jan/22 $$\mathrm{if}\mathrm{a};\mathrm{b};\mathrm{c}<0\mathrm{and}\mathrm{a}+\mathrm{b}+\mathrm{c}=3\mathrm{prove}\mathrm{that}:$$$${(1+\frac{\mathrm{b}}{\mathrm{a}})}^{\frac{1}{{\mathbf{b}}^2}}\cdot {(1+\frac{\mathrm{c}}{\mathrm{b}})}^{\frac{1}{{\mathbf{c}}^2}}\cdot {(1+\frac{\mathrm{a}}{\mathrm{c}})}^{\frac{1}{{\mathbf{a}}^2}}⩾8$$ Terms of Service Privacy Policy…

Question Number 164405 by Zaynal last updated on 16/Jan/22 $$\mathit{l}\mathit{e}\mathit{t}\mathit{a},\mathit{b},\mathit{c}>0;\mathit{a}+\mathit{b}+\mathit{c}=3$$$$\boldsymbol{{prove}}\:\boldsymbol{{that}};\:\frac{\boldsymbol{{a}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} \:+\:\boldsymbol{{bc}}\:+\:\boldsymbol{{c}}^{\mathrm{2}} }\:\:+\:\:\frac{\boldsymbol{{b}}^{\mathrm{2}} }{\boldsymbol{{c}}^{\mathrm{2}} \:+\:\boldsymbol{{ac}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} \:}\:\:+\:\:\frac{\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} \:+\boldsymbol{{ba}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} }\:\:\mathrm{6}\:\:\geqslant\:\:\mathrm{2}\boldsymbol{{abc}}\:\:+\:\:\frac{\mathrm{5}}{\mathrm{3}}\:\:\left(\boldsymbol{{a}}^{\mathrm{2}} \:+\:\boldsymbol{{b}}^{\mathrm{2}} \:+\:\boldsymbol{{c}}^{\mathrm{2}} \:\right)\:\:\geqslant\:\:\mathrm{7} \…