Category: Algebra

Question Number 16589 by ajfour last updated on 24/Jun/17 $${\mathrm{x}}^2-\mid 3\mathrm{x}+2\mid +\mathrm{x}⩾0$$$$\mathrm{find}\mathrm{range}\mathrm{of}\mathrm{values}\mathrm{of}\mathrm{x}\mathrm{agreeing}$$$$\mathrm{with}\mathrm{above}\mathrm{inequality}.$$ Answered by mrW1 last updated on 24/Jun/17 $$\mathrm{if}\:\mathrm{3x}+\mathrm{2}\geqslant\mathrm{0}\:\mathrm{or}\:\mathrm{x}\geqslant−\frac{\mathrm{2}}{\mathrm{3}}\:\left(\approx−\mathrm{0}.\mathrm{67}\right)…

Question Number 147621 by mathdanisur last updated on 22/Jul/21 $$Findthegeneralsolutionfor:$$$$\frac{dy}{dx}={(3x+2y+1)}^2$$ Answered by gsk2684 last updated on 22/Jul/21 $$putu=3x+2y+1\Rightarrow \frac{du}{dx}=3+2\frac{dy}{dx}$$$$\frac{{du}}{{dx}}=\mathrm{3}+\mathrm{2}{u}^{\mathrm{2}} \…

Question Number 82082 by TawaTawa last updated on 18/Feb/20 $$\mathrm{Evaluate}:{\left(\frac{\sqrt{30+\sqrt{8}+\sqrt{5}}}{\sqrt{8}+\sqrt{5}}\right)}^{1/4}$$ Commented by MJS last updated on 18/Feb/20 $${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{not}\mathrm{possible}\mathrm{to}\mathrm{expand}\mathrm{or}\mathrm{factorise}\sqrt{30+\sqrt{8}+\sqrt{5}}$$$$\Rightarrow \mathrm{we}\mathrm{can}\mathrm{only}\mathrm{use}\mathrm{a}\mathrm{calculator}$$ Commented…

Question Number 147611 by mathdanisur last updated on 22/Jul/21 $${\left(111\right)}_{10}={\left(x\right)}_5$$$$\Rightarrow x=?$$ Answered by bobhans last updated on 22/Jul/21 $$\left(\mathrm{111}\right)_{\mathrm{10}} =\:\mathrm{1}×\mathrm{10}^{\mathrm{2}} +\mathrm{1}×\mathrm{10}^{\mathrm{1}}…

Question Number 82071 by jagoll last updated on 18/Feb/20 $$x\ne y\ne z\ne 0$$$$xy+xz+yz=0$$$$provethat\frac{x+y}{z}+\frac{x+z}{y}+\frac{y+z}{x}=-3$$$$$$ Answered by TANMAY PANACEA last updated on…