Category: Algebra

Question Number 216270 by MATHEMATICSAM last updated on 02/Feb/25 $$\mathrm{If}(b-c)x+(c-a)y+(a-b)z=0\mathrm{then}$$$$\mathrm{prove}\mathrm{that}\frac{b-c}{y-z}=\frac{c-a}{z-x}=\frac{a-b}{x-y}.$$ Answered by Rasheed.Sindhi last updated on 02/Feb/25 $$\mathrm{If}(b-c)x+(c-a)y+(a-b)z=0\mathrm{then}$$$$\mathrm{prove}\:\mathrm{that}\:\frac{{b}\:−\:{c}}{{y}\:−\:{z}}\:=\:\frac{{c}\:−\:{a}}{{z}\:−\:{x}}\:=\:\frac{{a}\:−\:{b}}{{x}\:−\:{y}}\:. \…

Question Number 216253 by MATHEMATICSAM last updated on 01/Feb/25 $$\mathrm{If}x\mathrm{is}\mathrm{a}\mathrm{positive}\mathrm{acute}\mathrm{angle}\mathrm{and}$$$$\sin x+{\sin }^{2}x+{\sin }^{3}x=1\mathrm{then}\mathrm{find}$$$$\mathrm{minimum}\mathrm{value}\mathrm{of}{\cot }^{2}x.$$ Commented by Frix last updated on…

Question Number 216242 by ajfour last updated on 01/Feb/25 $${(x-a)}^2+{(x^2-a)}^2=a^2$$$$Findx,givena.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 216183 by MATHEMATICSAM last updated on 29/Jan/25 Answered by A5T last updated on 29/Jan/25 $$={\mathrm{a}}^3-{\mathrm{a}}^2(\mathrm{b}+\mathrm{c})+{\mathrm{b}}^3+{\mathrm{c}}^3+2\mathrm{abc}-{\mathrm{b}}^2(\mathrm{a}+\mathrm{c})-{\mathrm{c}}^2(\mathrm{a}+\mathrm{b})$$$$=\mathrm{a}^{\mathrm{2}}…

Question Number 216076 by efronzo1 last updated on 27/Jan/25 $$\frac{\lfloor \frac{\mathrm{x}}{3}\rfloor }{\lfloor \frac{\mathrm{x}}{4}\rfloor }=\frac{21}{16};\mathrm{x}=?$$ Answered by mr W last updated on 28/Jan/25 $$\lfloor \frac{x}{3}\rfloor =21k$$$$\lfloor \frac{x}{4}\rfloor =16k\ne 0\Rightarrow k\ne 0$$$$\frac{{x}}{\mathrm{3}}=\mathrm{21}{k}+{a}\:{with}\:\mathrm{0}\leqslant{a}<\mathrm{1}…