Menu Close

Category: Algebra

Solve-the-system-of-equation-x-2-yz-52-i-y-2-xz-6-ii-z-2-xy-86-iii-

Question Number 6105 by sanusihammed last updated on 13/Jun/16 $${Solve}\:{the}\:{system}\:{of}\:{equation}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:−\:{yz}\:=\:−\:\mathrm{52}\:\:\:…………..\:\left({i}\right) \\ $$$${y}^{\mathrm{2}} \:−\:{xz}\:=\:−\:\mathrm{6}\:…………….\:\left({ii}\right) \\ $$$${z}^{\mathrm{2}} \:−\:{xy}\:=\:\mathrm{86}\:\:\:…………..\:\left({iii}\right) \\ $$ Commented by…

Question-137117

Question Number 137117 by MathZa last updated on 29/Mar/21 Answered by mathmax by abdo last updated on 30/Mar/21 $$\mathrm{is}\:\mathrm{z}+\mathrm{i}\sqrt{\mathrm{2}}=\mathrm{0}? \\ $$$$\mathrm{z}+\mathrm{i}\sqrt{\mathrm{2}}=\frac{\mathrm{2}−\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}}\mathrm{i}}{\mathrm{1}+\sqrt{\mathrm{2}}\mathrm{i}−\mathrm{i}}\:+\sqrt{\mathrm{2}}\mathrm{i}\:=\frac{\mathrm{2}−\sqrt{\mathrm{2}}+\sqrt{\mathrm{2}}\mathrm{i}+\sqrt{\mathrm{2}}\mathrm{i}−\mathrm{2}+\sqrt{\mathrm{2}}}{\mathrm{1}+\sqrt{\mathrm{2}}\mathrm{i}\:−\mathrm{i}} \\ $$$$=\frac{\mathrm{2}\sqrt{\mathrm{2}}\mathrm{i}}{\mathrm{1}+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{i}}\:=\frac{\mathrm{2}\sqrt{\mathrm{2}}\mathrm{i}\left(\mathrm{1}−\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{i}\right.}{\mathrm{1}+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} }\:=\frac{\mathrm{2}\sqrt{\mathrm{2}}\mathrm{i}+\mathrm{2}\sqrt{\mathrm{2}}\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)}{\mathrm{1}+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} }…

Three-interior-angles-of-a-nonagon-are-equal-and-the-sum-of-the-other-six-is-1050-Find-the-size-of-one-of-the-equal-angles-

Question Number 71533 by pete last updated on 16/Oct/19 $$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{nonagon}\:\mathrm{are} \\ $$$$\mathrm{equal}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{six}\:\mathrm{is}\:\mathrm{1050}° \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{size}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equal}\:\mathrm{angles}. \\ $$ Answered by MJS last updated on 17/Oct/19 $$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{is}\:\mathrm{1260}° \\…

a-number-consists-of-digits-1-and-2-the-sum-of-its-digits-is-2018-if-the-number-is-multiplied-with-5-the-sum-of-the-digits-will-be-10000-find-how-many-digits-this-number-has-

Question Number 71534 by mr W last updated on 16/Oct/19 $${a}\:{number}\:{consists}\:{of}\:{digits}\:\mathrm{1}\:{and}\:\mathrm{2}. \\ $$$${the}\:{sum}\:{of}\:{its}\:{digits}\:{is}\:\mathrm{2018}. \\ $$$${if}\:{the}\:{number}\:{is}\:{multiplied}\:{with}\:\mathrm{5},\: \\ $$$${the}\:{sum}\:{of}\:{the}\:{digits}\:{will}\:{be}\:\mathrm{10000}. \\ $$$${find}\:{how}\:{many}\:{digits}\:{this}\:{number} \\ $$$${has}. \\ $$ Answered by…