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Question Number 159863 by HongKing last updated on 21/Nov/21 $$\mathrm{Dertermine}\:\mathrm{all}\:\mathrm{pairs}\:\left(\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}}\right)\:\mathrm{of}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{2010x}\:-\:\mathrm{xy}\:+\:\mathrm{2012y}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by mr W last updated on 21/Nov/21 $$\left({x}−\mathrm{2012}\right){y}=\mathrm{1}+\mathrm{2010}{x}…
Question Number 159860 by Khalmohmmad last updated on 21/Nov/21 Commented by MJS_new last updated on 22/Nov/21 $${t}+{t}^{−\mathrm{1}} =−\mathrm{1} \\ $$$${t}^{\mathrm{2}} +{t}+\mathrm{1}=\mathrm{0}\:\Rightarrow\:\mathrm{no}\:\mathrm{real}\:\mathrm{solution} \\ $$$${t}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{i} \\ $$$${t}^{\mathrm{1402}}…
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Question Number 159842 by abdullah_ff last updated on 21/Nov/21 $$\mathrm{if}\:{p}−\mathrm{5}\:=\:\mathrm{2}\sqrt{\mathrm{6}}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${p}\sqrt{{p}}−\frac{\mathrm{1}}{{p}\sqrt{{p}}}\:=\:\mathrm{22}\sqrt{\mathrm{2}} \\ $$ Commented by tounghoungko last updated on 21/Nov/21 $${false} \\ $$ Commented…
Question Number 28739 by NECx last updated on 29/Jan/18 $${if}\:{S}_{{n}} =\frac{{a}\left({r}^{{n}} −\mathrm{1}\right)}{{r}−\mathrm{1}}\: \\ $$$$ \\ $$$${make}\:{r}\:{the}\:{subject}\:{of}\:{formula} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Answered…
Question Number 94257 by pete last updated on 17/May/20 $$\mathrm{If}\:\mathrm{9y}^{\mathrm{2}} +\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\:=\mathrm{3},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{27y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} } \\ $$ Answered by niroj last updated on 17/May/20…
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Question Number 159777 by abdullah_ff last updated on 21/Nov/21 $$\mathrm{if}\:{x}\:+\:{y}\:=\:\sqrt{\mathrm{7}}\:\mathrm{and}\:{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:=\:\sqrt{\mathrm{35}}\:; \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{16}{xy}\left({x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \right) \\ $$ Commented by abdullah_ff last updated on 21/Nov/21…
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