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Category: Algebra

Question-152596

Question Number 152596 by liberty last updated on 30/Aug/21 Answered by som(math1967) last updated on 30/Aug/21 $$\boldsymbol{{let}}\:\frac{\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}}{\mathrm{4}\boldsymbol{{y}}+\mathrm{3}}=\frac{\mathrm{4}\boldsymbol{{y}}+\mathrm{1}}{\mathrm{9}}=\frac{\mathrm{11}}{\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}}=\boldsymbol{{k}} \\ $$$$\left[\because\boldsymbol{{a}}=\boldsymbol{{b}}=\boldsymbol{{c}}\right] \\ $$$$\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}=\boldsymbol{{k}}\left(\mathrm{4}\boldsymbol{{y}}+\mathrm{3}\right) \\ $$$$\mathrm{4}\boldsymbol{{y}}+\mathrm{1}=\mathrm{9}\boldsymbol{{k}} \\ $$$$\mathrm{11}=\boldsymbol{{k}}\left(\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}\right)…

what-are-the-roots-of-the-system-of-equation-x-y-y-x-1-4-3-and-x-y-xy-5-

Question Number 87050 by jagoll last updated on 02/Apr/20 $$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equation}\:\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}+\mathrm{1}}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{and}\:\mathrm{x}+\mathrm{y}\:+\:\mathrm{xy}\:=\:\mathrm{5}\:? \\ $$ Commented by john santu last updated on 02/Apr/20 $$\Rightarrow{x}+{y}+{xy}+\mathrm{1}\:=\:\mathrm{6}\:\Rightarrow{x}\left({y}+\mathrm{1}\right)=\mathrm{5}−{y}…

If-a-b-c-0-then-a-b-b-c-a-c-abc-is-equal-to-

Question Number 21471 by Joel577 last updated on 24/Sep/17 $$\mathrm{If}\:\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{0},\:\mathrm{then} \\ $$$$\frac{\left({a}\:+\:{b}\right)\left({b}\:+\:{c}\right)\left({a}\:+\:{c}\right)}{{abc}}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:… \\ $$ Answered by Tinkutara last updated on 24/Sep/17 $${a}+{b}=−{c} \\ $$$$\therefore\frac{\left({a}+{b}\right)\left({b}+{c}\right)\left({c}+{a}\right)}{{abc}}=\frac{\left(−{c}\right)\left(−{a}\right)\left(−{b}\right)}{{abc}}=−\mathrm{1} \\…