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Category: Algebra

If-x-a-2-bc-y-b-2-ca-z-c-2-ab-then-prove-that-x-3-y-3-z-3-3xyz-is-a-perfect-square-

Question Number 179157 by Agnibhoo98 last updated on 25/Oct/22 $$\mathrm{If}\:{x}\:=\:{a}^{\mathrm{2}} −\:{bc},\:{y}\:=\:{b}^{\mathrm{2}} \:−\:{ca},\:{z}\:=\:{c}^{\mathrm{2}} \:−\:{ab} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}, \\ $$$${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \:−\:\mathrm{3}{xyz}\:\mathrm{is}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$ Answered by som(math1967)…

1-3a-1-4b-1-6c-and-a-b-c-27-find-a-c-

Question Number 179140 by Shrinava last updated on 25/Oct/22 $$\frac{\mathrm{1}}{\mathrm{3a}}\:=\:\frac{\mathrm{1}}{\mathrm{4b}}\:=\:\frac{\mathrm{1}}{\mathrm{6c}}\:\:\:\mathrm{and}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{27} \\ $$$$\mathrm{find}\:\:\:\mathrm{a}−\mathrm{c}=? \\ $$ Answered by Frix last updated on 25/Oct/22 $${a}=\mathrm{4}{t} \\ $$$${b}=\mathrm{3}{t} \\…

solve-x-2-1-1-2-x-6-18-0-

Question Number 48075 by MJS last updated on 19/Nov/18 $$\mathrm{solve}\:\:\:\:\:\left(\mid{x}^{\mathrm{2}} −\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{2}}\right){x}+\frac{\sqrt{\mathrm{6}}}{\mathrm{18}}=\mathrm{0} \\ $$ Commented by MJS last updated on 19/Nov/18 $$\mathrm{case}\:\mathrm{1} \\ $$$${x}<−\mathrm{1} \\ $$$${x}^{\mathrm{3}}…

Solve-the-system-x-3-x-2-y-4xy-2-4y-3-0-x-2-2xy-3y-2-x-y-0-

Question Number 48055 by F_Nongue last updated on 21/Nov/18 $${Solve}\:{the}\:{system}: \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}−\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{3}} =\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} −{x}−{y}=\mathrm{0}}\end{cases} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated…

1-Compare-pi-2022e-and-e-2022-2-Compute-value-of-P-pi-

Question Number 179105 by Shrinava last updated on 24/Oct/22 $$\mathrm{1}.\:\mathrm{Compare}:\:\:\:\pi^{\mathrm{2022}\boldsymbol{\mathrm{e}}} \:\:\:\mathrm{and}\:\:\:\mathrm{e}^{\mathrm{2022}\boldsymbol{\pi}} \\ $$$$\mathrm{2}.\:\mathrm{Compute}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{P}\:=\:\pi^{\boldsymbol{\pi}^{\boldsymbol{\pi}^{…^{\boldsymbol{\pi}} } } } \\ $$ Answered by MJS_new last updated on 25/Oct/22…

Given-a-gt-0-b-gt-0-c-gt-2-a-b-1-find-the-minimum-value-of-3ac-b-c-ab-6-c-2-

Question Number 179090 by CrispyXYZ last updated on 24/Oct/22 $$\mathrm{Given}\:{a}>\mathrm{0},\:{b}>\mathrm{0},\:{c}>\mathrm{2},\:{a}+{b}=\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\:\frac{\mathrm{3}{ac}}{{b}}+\frac{{c}}{{ab}}+\frac{\mathrm{6}}{{c}−\mathrm{2}}. \\ $$ Commented by Frix last updated on 24/Oct/22 $$\mathrm{24} \\ $$ Answered…