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Category: Algebra

Question-90160

Question Number 90160 by A8;15: last updated on 21/Apr/20 Answered by TANMAY PANACEA. last updated on 21/Apr/20 $${put}\:{x}=\mathrm{1}\:{in}\:{RHS} \\ $$$$\sqrt{\mathrm{61}+\mathrm{6}−\mathrm{3}}\:=\mathrm{8} \\ $$$${put}\:{x}=\mathrm{1}\:{LHS} \\ $$$$\mathrm{16}^{\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:}\right)^{\mathrm{2}} }…

x-2021-3-2019-3-x-2-6-

Question Number 90139 by jagoll last updated on 21/Apr/20 $$\mathrm{x}\:=\:\mathrm{2021}^{\mathrm{3}} −\mathrm{2019}^{\mathrm{3}} \\ $$$$\sqrt{\frac{\mathrm{x}−\mathrm{2}}{\mathrm{6}}}\:=\:? \\ $$ Commented by jagoll last updated on 21/Apr/20 $$\mathrm{x}\:=\:\left(\mathrm{p}+\mathrm{2}\right)^{\mathrm{3}} −\mathrm{p}^{\mathrm{3}} \:,\:\mathrm{p}\:=\:\mathrm{2019}…

Solve-for-real-numbers-x-a-x-b-a-x-x-b-x-a-b-x-a-b-R-and-a-b-

Question Number 155650 by mathdanisur last updated on 03/Oct/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\sqrt{\frac{\mathrm{x}-\mathrm{a}}{\mathrm{x}-\mathrm{b}}}\:+\:\frac{\mathrm{a}}{\mathrm{x}}\:=\:\sqrt{\frac{\mathrm{x}-\mathrm{b}}{\mathrm{x}-\mathrm{a}}}\:+\:\frac{\mathrm{b}}{\mathrm{x}} \\ $$$$\mathrm{a};\mathrm{b}\in\mathbb{R}\:\:\mathrm{and}\:\:\mathrm{a}\neq\mathrm{b} \\ $$ Answered by som(math1967) last updated on 03/Oct/21 $$\sqrt{\frac{{x}−{a}}{{x}−{b}}}−\sqrt{\frac{{x}−{b}}{{x}−{a}}}=\frac{{b}−{a}}{{x}} \\…

if-a-b-c-0-and-a-b-c-1-prove-that-18-ab-45-a-2-b-11-

Question Number 155653 by mathdanisur last updated on 03/Oct/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1}\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{18}\:\Sigma\:\mathrm{ab}\:+\:\mathrm{45}\:\Sigma\:\mathrm{a}^{\mathrm{2}} \mathrm{b}\:\leqslant\:\mathrm{11} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

y-ax-3-bx-2-cx-d-then-prove-that-the-equation-y-0-has-only-one-real-root-if-a-9ad-bc-2-4-b-2-3ac-c-2-3bd-gt-0-provided-b-2-gt-3ac-

Question Number 24565 by ajfour last updated on 21/Nov/17 $$\:\:\boldsymbol{{y}}=\boldsymbol{{ax}}^{\mathrm{3}} +\boldsymbol{{bx}}^{\mathrm{2}} +\boldsymbol{{cx}}+\boldsymbol{{d}}\:,\:{then} \\ $$$${prove}\:{that}\:{the}\:{equation}\:{y}=\mathrm{0} \\ $$$${has}\:{only}\:{one}\:{real}\:{root}\:{if} \\ $$$$\:\boldsymbol{{a}}\left[\left(\mathrm{9}\boldsymbol{{ad}}−\boldsymbol{{bc}}\right)^{\mathrm{2}} −\mathrm{4}\left(\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{ac}}\right)\left(\boldsymbol{{c}}^{\mathrm{2}} −\mathrm{3}\boldsymbol{{bd}}\right)\right] \\ $$$$\:\:\:\:>\:\mathrm{0}\:\:\:\:\:{provided}\:\:\:\boldsymbol{{b}}^{\mathrm{2}} \:>\:\mathrm{3}\boldsymbol{{ac}}\:. \\…