Category: Algebra

Question Number 13349 by tawa tawa last updated on 19/May/17 Answered by ajfour last updated on 19/May/17 $$forx\ne \frac{2}{a},wehave$$$$24x^2+25x-47=-(ax-2)(8x+3)-53$$$$\mathrm{24}{x}^{\mathrm{2}} +\mathrm{25}{x}−\mathrm{47}=−\mathrm{8}{ax}^{\mathrm{2}} +\left(\mathrm{16}−\mathrm{3}{a}\right){x}+\mathrm{6}−\mathrm{53}…

Question Number 78877 by M±th+et£s last updated on 21/Jan/20 $$if\frac{sin\left(A\right)}{sin\left(B\right)}=\frac{sin\left(D\right)}{sin\left(C\right)}$$$$andA+B=C+D$$$$$$$$thenprovethat$$$$A+B=180$$$$C+D=180$$$$$$ Commented…

Question Number 13333 by mrW1 last updated on 19/May/17 $$Aboutthesolutiontoquestion:$$$$Fora,b,c>0andabc=1,prove$$$$a^{b+c}{b}^{c+a}{c}^{a+b}⩽1$$$$$$$$Way1:$$$${Let}^{\prime }ssaya⩽b⩽c.$$$${We}\:{can}\:{prove}\:{that}\:{a}\leqslant\mathrm{1}:…

Question Number 13327 by Nayon last updated on 18/May/17 $$howcanweexpand{(1+x)}^{\frac{1}{2}}??$$ Answered by prakash jain last updated on 19/May/17 $$\left(\mathrm{1}+{x}\right)^{{y}} =\mathrm{1}+{yx}+\frac{{y}\left({y}−\mathrm{1}\right)}{\mathrm{2}!}{x}^{\mathrm{2}} +\frac{{y}\left({y}−\mathrm{1}\right)\left({y}−\mathrm{2}\right)}{\mathrm{3}!}{x}^{\mathrm{3}} +…

Question Number 13294 by Tinkutara last updated on 17/May/17 $$\mathrm{If}a,b\mathrm{and}c\mathrm{are}\mathrm{the}\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{triangle}$$$$\mathrm{and}a+b+c=2,\mathrm{then}\mathrm{prove}\mathrm{that}$$$$a^2+b^2+c^2+2abc<2$$ Commented by prakash jain last updated…