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Category: Algebra

Question-116633

Question Number 116633 by zakirullah last updated on 05/Oct/20 Answered by Olaf last updated on 05/Oct/20 $$\mathrm{If}\:\mathrm{B}\:\mathrm{is}\:\mathrm{a}\:\mathrm{inverse}\:\mathrm{matrix}\:\mathrm{of}\:\mathrm{A} \\ $$$$\mathrm{then}\:\mathrm{B}.\mathrm{A}\:=\:\mathrm{A}.\mathrm{B}\:=\:\mathrm{I}\:\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{C}\:\mathrm{is}\:\mathrm{another}\:\mathrm{inverse}\:\mathrm{matrix}\:\mathrm{of}\:\mathrm{A} \\ $$$$\mathrm{then}\:\mathrm{C}.\mathrm{A}\:=\:\mathrm{A}.\mathrm{C}\:=\:\mathrm{I}\:\left(\mathrm{2}\right)…

Find-the-sum-of-the-solutions-of-the-equation-x-2-x-x-4-2-0-x-gt-0-

Question Number 182073 by Acem last updated on 04/Dec/22 $${Find}\:{the}\:{sum}\:{of}\:{the}\:{solutions}\:{of}\:{the}\:{equation}: \\ $$$$\:\mid\sqrt{{x}}\:−\:\mathrm{2}\mid+\:\sqrt{{x}}\:\left(\sqrt{{x}}\:−\:\mathrm{4}\right)+\:\mathrm{2}=\:\mathrm{0}\:\:\:;\:{x}>\:\mathrm{0} \\ $$ Answered by HeferH last updated on 04/Dec/22 $$\:\mid\sqrt{{x}}\:−\:\mathrm{2}\mid\:=\:\mathrm{4}\sqrt{{x}}\:−\:{x}\:−\:\mathrm{2} \\ $$$$\:\:\sqrt{{x}}\:−\:\mathrm{2}\:=\:\pm\:\left(\mathrm{4}\sqrt{{x}}\:−\:{x}\:−\:\mathrm{2}\right) \\…

Let-x-xy-y-54-x-y-N-Find-x-y-

Question Number 182074 by Acem last updated on 04/Dec/22 $${Let}\:{x}+\:{xy}+\:{y}=\:\mathrm{54}\:\:\:;\:{x},\:{y}\in\:\mathbb{N}\:,\:{Find}\:{x}+\:{y} \\ $$ Answered by HeferH last updated on 04/Dec/22 $${x}\:+\:{xy}\:+\:{y}\:=\:\mathrm{54} \\ $$$$\:{x}\left(\mathrm{1}\:+\:{y}\right)\:+\:{y}\:=\:\mathrm{54} \\ $$$$\:{x}\left(\mathrm{1}\:+\:{y}\right)\:+\:\left(\mathrm{1}\:+\:{y}\right)\centerdot\mathrm{1}\:=\:\mathrm{55} \\…