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Category: Algebra

1-a-1-b-9-1-a-1-3-1-b-1-3-1-1-a-1-3-1-1-b-1-3-18-8a-4b-

Question Number 161484 by bobhans last updated on 18/Dec/21 $$\:\:\begin{cases}{\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}=\mathrm{9}}\\{\left(\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{a}}}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{b}}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{a}}}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{b}}}\right)=\mathrm{18}}\end{cases} \\ $$$$\:\:\:\mathrm{8a}+\mathrm{4b}=? \\ $$ Answered by mr W last updated on 18/Dec/21 $${let}\:{A}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{a}}},\:{B}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{b}}} \\ $$$${let}\:{p}={A}+{B},\:{q}={AB}…

54-x-1-3-54-x-1-3-18-1-3-x-

Question Number 95920 by bobhans last updated on 28/May/20 $$\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}+\sqrt{\mathrm{x}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}−\sqrt{\mathrm{x}}}\:=\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{18}}\: \\ $$$$\mathrm{x}\:=\:?\: \\ $$ Answered by i jagooll last updated on 28/May/20 $$\mathrm{let}\:\mathrm{a}\:=\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}+\sqrt{\mathrm{x}}}\:,\:\mathrm{b}\:=\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}−\sqrt{\mathrm{x}}}\: \\ $$$$\mathrm{a}+\mathrm{b}\:=\:\frac{\mathrm{a}^{\mathrm{3}}…

if-x-y-z-gt-0-such-that-x-y-z-3-and-0-then-prove-that-x-y-3-y-2-y-z-3-z-2-z-x-3-x-2-3-1-

Question Number 161433 by HongKing last updated on 17/Dec/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{3} \\ $$$$\mathrm{and}\:\:\boldsymbol{\lambda}\geqslant\mathrm{0}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}}{\mathrm{y}^{\mathrm{3}} +\lambda\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}}{\mathrm{z}^{\mathrm{3}} +\lambda\mathrm{z}^{\mathrm{2}} }\:+\:\frac{\mathrm{z}}{\mathrm{x}^{\mathrm{3}} +\lambda\mathrm{x}^{\mathrm{2}} }\:\geqslant\:\frac{\mathrm{3}}{\lambda+\mathrm{1}} \\ $$ Terms of Service…