Category: Algebra

Question Number 121913 by Jamshidbek2311 last updated on 12/Nov/20 $$\{\begin{array}{l}{x}^2+y=36\\ x+y^2=25x=?y=?\end{array}$$ Answered by MJS_new last updated on 12/Nov/20 $$\left(1\right)y=36-x^2$$$$\Rightarrow \…

Question Number 187442 by Shrinava last updated on 17/Feb/23 $$\mathrm{If}\frac{7^{\mathbf{x}}}{1+7^{\mathbf{x}}}=\frac{3}{7}\mathrm{find}\frac{{2401}^{\mathbf{x}}}{1+{2401}^{\mathbf{x}}}=?$$ Answered by Rasheed.Sindhi last updated on 17/Feb/23 $$\frac{\mathrm{7}^{\boldsymbol{{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{{x}}}…

Question Number 121890 by oustmuchiya@gmail.com last updated on 12/Nov/20 Commented by liberty last updated on 12/Nov/20 $$\left(\mathrm{v}\right)\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{1}} \right)^{\mathrm{12}} \:=\:\underset{\mathrm{r}\:=\:\mathrm{0}} {\overset{\mathrm{12}} {\sum}}$$\left(\begin{array}{c}12\\ \mathrm{r}\end{array}\right)$$\:\left(\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{12}−\mathrm{r}} .\left(\mathrm{x}^{−\mathrm{1}} \right)^{\mathrm{r}}…

Question Number 121889 by oustmuchiya@gmail.com last updated on 12/Nov/20 Answered by Dwaipayan Shikari last updated on 12/Nov/20 $${(1+ax)}^b=1+48x+1008x^2+\dots$$$$ab=48$$$${a}^{\mathrm{2}} \frac{{b}\left({b}−\mathrm{1}\right)}{\mathrm{2}}=\mathrm{1008}…

Question Number 187388 by ajfour last updated on 16/Feb/23 $$p^3+q^3=c,pq=\frac{1}{3}\mathrm{\forall }0<c<\frac{2}{3\sqrt{3}}$$$$Findp+q.$$ Answered by anurup last updated on 17/Feb/23 $$ \…