Menu Close

Category: Algebra

a-b-c-R-and-a-b-c-and-a-b-c-b-a-c-c-a-b-are-three-consecutive-terms-of-AP-Arithmetic-progression-find-b-2-a-2-c-2-b-2-

Question Number 171403 by mnjuly1970 last updated on 14/Jun/22 $$\:\:{a}\:,\:{b}\:,\:{c}\:\in\mathbb{R}\:\:{and}\:\:{a}\neq{b}\neq{c} \\ $$$$\:\:{and}\:\:\:\frac{{a}}{{b}+{c}}\:,\:\frac{{b}}{{a}+{c}}\:,\:\frac{{c}}{{a}+{b}}\:\:\:{are}\:{three}\:{consecutive}\:{terms}\:{of}\:{AP} \\ $$$$\:\:\left({Arithmetic}\:{progression}\:\right) \\ $$$$\:\:{find}\:−:\:\:\:\frac{{b}^{\:\mathrm{2}} −{a}^{\:\mathrm{2}} }{{c}^{\:\mathrm{2}} −{b}^{\:\mathrm{2}} } \\ $$ Answered by Rasheed.Sindhi…

a-b-and-c-are-positive-real-numbers-such-that-a-2-ab-b-2-3-25-b-2-3-c-2-9-and-c-2-ca-a-2-16-find-the-value-of-ab-2bc-3ac-

Question Number 171388 by infinityaction last updated on 15/Jun/22 $${a},{b},\:{and}\:{c}\:{are}\:{positive}\:{real}\:{numbers} \\ $$$${such}\:{that} \\ $$$${a}^{\mathrm{2}} +{ab}+\frac{{b}^{\mathrm{2}} }{\mathrm{3}}\:=\:\mathrm{25}\:\:,\:\:\:\:\frac{{b}^{\mathrm{2}} }{\mathrm{3}}\:+\:{c}^{\mathrm{2}} \:=\mathrm{9} \\ $$$${and}\:{c}^{\mathrm{2}} +{ca}+{a}^{\mathrm{2}} \:=\:\mathrm{16} \\ $$$${find}\:\:{the}\:\:{value}\:{of}\:\:{ab}+\mathrm{2}{bc}+\mathrm{3}{ac} \\…

Each-of-the-students-in-the-class-was-in-the-theater-exactly-two-times-during-the-winter-holidays-while-performances-A-B-and-C-were-seen-by-25-12-and-23-students-respectively-How-many-students-are-

Question Number 105851 by 1549442205PVT last updated on 01/Aug/20 $$\mathrm{Each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{class}\:\mathrm{was} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{theater}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{times}\:\mathrm{during}\: \\ $$$$\:\mathrm{the}\:\mathrm{winter}\:\mathrm{holidays},\mathrm{while} \\ $$$$\mathrm{performances}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{were}\:\mathrm{seen}\:\mathrm{by} \\ $$$$\mathrm{25},\mathrm{12}\:\mathrm{and}\:\mathrm{23}\:\mathrm{students},\mathrm{respectively} \\ $$$$.\mathrm{How}\:\mathrm{many}\:\mathrm{students}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{class}?\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{them}\:\mathrm{saw}\:\mathrm{performances} \\ $$$$\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\mathrm{B}\:\mathrm{and}\:\mathrm{C},\mathrm{C}\:\mathrm{and}\:\mathrm{A}? \\…

Question-40306

Question Number 40306 by behi83417@gmail.com last updated on 19/Jul/18 Commented by MJS last updated on 20/Jul/18 $$\mathrm{can}\:\mathrm{we}\:\mathrm{show}\:\mathrm{the}\:\mathrm{following}? \\ $$$$\frac{\mathrm{3}}{\mathrm{2}}\leqslant\frac{{x}^{\mathrm{2}} +{yz}}{{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} +{xz}}{{x}^{\mathrm{2}} +{z}^{\mathrm{2}} }+\frac{{z}^{\mathrm{2}}…