Question Number 71082 by aliesam last updated on 11/Oct/19 $${prove}\:{that}\: \\ $$$$ \\ $$$$\mid\:\sqrt{\mid{x}\mid}\:−\:\sqrt{\mid{y}\mid}\:\mid\:\leqslant\:\sqrt{\mid{x}−{y}\mid}\: \\ $$$$ \\ $$ Answered by Henri Boucatchou last updated on…
Question Number 71089 by 20190927 last updated on 11/Oct/19 $$\left(\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}\right)^{\mathrm{x}} +\left(\sqrt{\sqrt{\mathrm{2}}+\mathrm{1}}\right)^{\mathrm{x}} =\mathrm{4} \\ $$ Answered by Henri Boucatchou last updated on 11/Oct/19 $$\:\sqrt{\mathrm{2}}\:+\:\mathrm{1}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\mathrm{1}},\:\boldsymbol{{let}}\:\:\boldsymbol{{a}}\:=\:\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}} \\ $$$$\:\left(\sqrt{\sqrt{\mathrm{2}}\:−\mathrm{1}}\right)^{\boldsymbol{{x}}}…
Question Number 136614 by bemath last updated on 24/Mar/21 $${If}\:{a}+\frac{\mathrm{1}}{{a}}\:=\:\mathrm{23}\:{then}\:\sqrt[{\mathrm{4}}]{{a}}\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{a}}}\:=? \\ $$ Answered by mr W last updated on 24/Mar/21 $${a}+\frac{\mathrm{1}}{{a}}=\left(\sqrt{{a}}+\frac{\mathrm{1}}{\:\sqrt{{a}}}\right)^{\mathrm{2}} −\mathrm{2}=\mathrm{23} \\ $$$$\sqrt{{a}}+\frac{\mathrm{1}}{\:\sqrt{{a}}}=\mathrm{5} \\…
Question Number 71073 by TawaTawa last updated on 11/Oct/19 Commented by Prithwish sen last updated on 11/Oct/19 $$\mathrm{a}^{\mathrm{2}} =\:\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{2bc} \\ $$$$\therefore\:\boldsymbol{\mathrm{bc}}\:=\:\frac{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} −\boldsymbol{\mathrm{c}}^{\mathrm{2}}…
Question Number 136607 by EDWIN88 last updated on 23/Mar/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:\mathrm{if}\:\mathrm{ax}+\mathrm{by}=\mathrm{3} \\ $$$$\mathrm{bx}−\mathrm{ay}\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$ Answered by MJS_new last updated on 24/Mar/21…
Question Number 5532 by Rasheed Soomro last updated on 18/May/16 $$\mathrm{Volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{and}\:\mathrm{its}\:\mathrm{surface}-\mathrm{area} \\ $$$$\mathrm{are}\:\mathrm{numerically}\:\mathrm{equal}.\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{measure}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}? \\ $$$$ \\ $$ Commented by FilupSmith last updated on…
Question Number 5531 by Rasheed Soomro last updated on 18/May/16 $$\mathrm{Once}\:\mathrm{I}\:\mathrm{opened}\:\mathrm{an}\:\mathrm{algebra}-\mathrm{book}.\mathrm{Instead} \\ $$$$\mathrm{of}\:\mathrm{individual}\:\mathrm{page}\:\mathrm{numbers}\:\mathrm{there}\:\mathrm{was} \\ $$$$\mathrm{written}:“{sum}\:{of}\:{page}\:{numbers}\:\:{infront} \\ $$$${of}\:{you}\:{is}\:\mathrm{x}''.\mathrm{Determine}\:\mathrm{the}\:\mathrm{page}\:\mathrm{numbers} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}. \\ $$ Commented by prakash jain…
Question Number 5525 by sanusihammed last updated on 17/May/16 $${Expand}\:\:{f}\left({z}\right)\:=\:{cos}\left({z}\right) \\ $$$${about}\:{point}\:\:{z}\:=\:\Pi/\mathrm{3} \\ $$$$ \\ $$$$ \\ $$ Commented by Yozzii last updated on 18/May/16…
Question Number 5508 by selene rmz. last updated on 17/May/16 $$\mathrm{24}\boldsymbol{\div}\mathrm{56} \\ $$ Answered by Abdul Haque Soomro last updated on 20/May/16 $$\mathrm{3}\boldsymbol{\div}\mathrm{7} \\ $$…
Question Number 5498 by Yozzii last updated on 16/May/16 $$\left(\mathrm{1}+{abc}\right)^{\mathrm{3}} \geqslant{abc}\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)\: \\ $$$${if}\:{a},{b},{c}>\mathrm{0}? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 Commented by…