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Category: Algebra

If-x-y-and-z-are-numbers-integers-different-of-0-49x-7y-z-0-25x-5y-z-0-find-y-2-4xz-

Question Number 112461 by dw last updated on 08/Sep/20 $${If}\:\:\:{x},\:{y}\:{and}\:{z}\:\:{are}\:{numbers}\:\:{integers}\:{different}\:{of}\:\:\:\mathrm{0} \\ $$$$\begin{cases}{\mathrm{49}{x}+\mathrm{7}{y}+{z}=\mathrm{0}}\\{\mathrm{25}{x}−\mathrm{5}{y}+{z}=\mathrm{0}}\end{cases}\:\:\:\:\:\:\:\:\:{find}\:\sqrt{{y}^{\mathrm{2}} −\mathrm{4}{xz}} \\ $$ Answered by floor(10²Eta[1]) last updated on 08/Sep/20 $$\mathrm{z}=\mathrm{5y}−\mathrm{25x} \\ $$$$\mathrm{49x}+\mathrm{7y}+\mathrm{5y}−\mathrm{25x}=\mathrm{24x}+\mathrm{12y}=\mathrm{0}\Rightarrow\mathrm{y}=−\mathrm{2x}…

Question-112408

Question Number 112408 by byaw last updated on 07/Sep/20 Commented by byaw last updated on 07/Sep/20 $$\mathrm{Please}\:\mathrm{help}\:\mathrm{to}\:\mathrm{use}\:\mathrm{latex}\:\mathrm{to}\:\mathrm{draw}\: \\ $$$$\mathrm{this}\:\mathrm{number}\:\mathrm{line}.\:\mathrm{Thank}\:\mathrm{you}. \\ $$ Terms of Service Privacy…

If-1-sin-x-sin-2-x-sin-3-x-4-2-3-0-lt-x-lt-pi-Find-the-value-of-x-

Question Number 177933 by Spillover last updated on 11/Oct/22 $$\mathrm{If}\:\mathrm{1}+\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+…\infty \\ $$$$=\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}\:\:,\mathrm{0}<\mathrm{x}<\pi\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$ \\ $$ Answered by Ar Brandon last updated on…

If-a-b-c-are-in-A-P-show-that-1-b-c-1-c-a-1-b-a-are-in-A-P-

Question Number 177932 by Spillover last updated on 11/Oct/22 $$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{c}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{c}}\:+\sqrt{\mathrm{a}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{a}}},\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P} \\ $$ Answered by Ar Brandon last updated on 11/Oct/22 $${a},\:{b},\:{c}\:\mathrm{in}\:{AP}\:\Rightarrow{b}−{a}={c}−{b}={d}\:\left(\mathrm{common}\:\mathrm{diff}\right) \\ $$$$\mathrm{If}\:{u}_{\mathrm{1}}…

Prove-that-x-3-y-3-x-y-2-3y-x-y-2-3xy-x-3-y-3-xy-x-2-y-2-xy-

Question Number 177928 by Spillover last updated on 11/Oct/22 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\left[\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} }{\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}} +\mathrm{3y}}\right]\boldsymbol{\div}\left[\frac{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} −\mathrm{3xy}}{\mathrm{x}^{\mathrm{3}} −\mathrm{y}^{\mathrm{3}} }\right]×\left[\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }\right]=\mathrm{xy} \\ $$ Answered by Ar…