Category: Algebra

Question Number 19688 by Tinkutara last updated on 14/Aug/17 $$\mathrm{The}\mathrm{vertices}\mathrm{of}\mathrm{a}\mathrm{square}\mathrm{are}{z}_1,z_2,z_3$$$$\mathrm{and}{z}_4\mathrm{taken}\mathrm{in}\mathrm{the}\mathrm{anticlockwise}\mathrm{order},$$$$\mathrm{then}{z}_3=$$$$\left(1\right)-{iz}_1+(1+i)z_2$$$$\left(\mathrm{2}\right)\:{iz}_{\mathrm{1}} \:+\:\left(\mathrm{1}\:+\:{i}\right){z}_{\mathrm{2}} \…

Question Number 19687 by Tinkutara last updated on 14/Aug/17 $$\mathrm{Let}{z}_1,z_2,z_3\mathrm{be}\mathrm{three}\mathrm{vertices}\mathrm{of}\mathrm{an}$$$$\mathrm{equilateral}\mathrm{triangle}\mathrm{circumscribing}\mathrm{the}$$$$\mathrm{circle}\mid z\mid =\frac{1}{2}.\mathrm{If}{z}_1=\frac{1}{2}+\frac{\sqrt{3}i}{2}\mathrm{and}{z}_1,$$$${z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{anticlockwise}\:\mathrm{sense}\:\mathrm{then}\:{z}_{\mathrm{2}} \:\mathrm{is} \…

Question Number 150719 by mathdanisur last updated on 14/Aug/21 Commented by MJS_new last updated on 15/Aug/21 $$\frac{1+\sqrt{21}}{2}⩽x+y⩽1+\sqrt{11}$$ Commented by mathdanisur last updated on…

Question Number 19643 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Find}\mathrm{the}\mathrm{real}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{equation}$$$$\sqrt{17+8x-2x^2}+\sqrt{4+12x-3x^2}=x^2$$$$-4x+13.$$ Answered by ajfour last updated on 13/Aug/17…

Question Number 19638 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Let}P\left(x\right)\mathrm{is}\mathrm{a}\mathrm{polynomial}\mathrm{such}\mathrm{that}$$$$P\left(1\right)=1,P\left(2\right)=2,P\left(3\right)=3,\mathrm{and}$$$$P\left(4\right)=5.\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}P\left(6\right).$$ Answered by ajfour last updated on 13/Aug/17 $$\mathrm{let}\:\mathrm{P}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{3}} +\mathrm{bx}^{\mathrm{2}}…