Category: Algebra

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} \…

Question Number 98859 by peter frank last updated on 16/Jun/20 Commented by mr W last updated on 16/Jun/20 $$p\left(x\right)=q\left(x\right)(x-1)$$$$p\left(1\right)=0$$$$1+c-2c+4=0$$$$\Rightarrow{c}=\mathrm{5}…

Question Number 98842 by  M±th+et+s last updated on 16/Jun/20 $$letf\left(x\right)beadolvnomialofdegree4$$$$suchthatf\left(1\right)=1,f\left(2\right)=2,f\left(3\right)=3,f\left(4\right)=4$$$$thenf\left(6\right)=?$$ Commented by mr W last updated on 16/Jun/20 $${see}\:{also}\:{Q}\mathrm{98268}…

Question Number 33307 by abdo imad last updated on 14/Apr/18 $$letz=x+iywithx\ne 0prove?that$$$$\mid \frac{e^z-1}{z}\mid ⩽\mid \frac{e^x-1}{x}\mid$$ Terms of Service Privacy Policy Contact: info@tinkutara.com