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Question Number 195118 Answers: 0 Comments: 1

a,b,c>0 & (1/a)+(1/b)+(1/c)=3 prove that (a/(b^2 +c^2 ))+(b/(a^2 +c^2 ))+(c/(a^2 +b^2 ))≥(3/2)(((a+b+c)/(ab+bc+ac)))^2

$${a},{b},{c}>\mathrm{0}\:\&\:\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}+\frac{\mathrm{1}}{{c}}=\mathrm{3} \\ $$$${prove}\:{that} \\ $$$$\frac{{a}}{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} }+\frac{{b}}{{a}^{\mathrm{2}} +{c}^{\mathrm{2}} }+\frac{{c}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\geqslant\frac{\mathrm{3}}{\mathrm{2}}\left(\frac{{a}+{b}+{c}}{{ab}+{bc}+{ac}}\right)^{\mathrm{2}} \\ $$

Question Number 195122 Answers: 0 Comments: 0

Question Number 195116 Answers: 0 Comments: 2

hi. please represntation (2)^(1/3) on number′s axis with ruler and compass and pen. thank you

$${hi}.\:{please}\:{represntation}\:\sqrt[{\mathrm{3}}]{\mathrm{2}}\:{on}\:{number}'{s}\:{axis} \\ $$$${with}\:{ruler}\:{and}\:{compass}\:{and}\:{pen}. \\ $$$${thank}\:{you} \\ $$

Question Number 195114 Answers: 2 Comments: 0

Σ_(k=3) ^(55) k=? 1)55 2)9k 3)53k 4)45

$$ \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\underset{\mathrm{k}=\mathrm{3}} {\overset{\mathrm{55}} {\sum}}\mathrm{k}=? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{5}\left.\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{9k}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{53k}\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right)\mathrm{45} \\ $$$$ \\ $$$$ \\ $$

Question Number 195121 Answers: 2 Comments: 0

x^2 −x−1=0 x^8 +2x^7 −47x=?

$${x}^{\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$${x}^{\mathrm{8}} +\mathrm{2}{x}^{\mathrm{7}} −\mathrm{47}{x}=? \\ $$

Question Number 195107 Answers: 1 Comments: 0

Question Number 195101 Answers: 2 Comments: 0

(√(ln2)) >^? ln2

$$\sqrt{{ln}\mathrm{2}}\:\:\overset{?} {>}{ln}\mathrm{2} \\ $$

Question Number 195097 Answers: 1 Comments: 0

Question Number 195094 Answers: 1 Comments: 0

Question Number 195093 Answers: 2 Comments: 0

Question Number 195087 Answers: 2 Comments: 0

Question Number 195083 Answers: 1 Comments: 0

x=(√5)−2 x+(1/x)=?

$${x}=\sqrt{\mathrm{5}}−\mathrm{2}\:\:\:\:\: \\ $$$${x}+\frac{\mathrm{1}}{{x}}=? \\ $$

Question Number 195082 Answers: 0 Comments: 0

Question Number 195079 Answers: 1 Comments: 0

Question Number 195075 Answers: 1 Comments: 0

lim_(x→∞) ((sin^2 x−cos^3 x)/x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}}{{x}} \\ $$

Question Number 195066 Answers: 0 Comments: 0

Question Number 195065 Answers: 2 Comments: 0

Question Number 195064 Answers: 0 Comments: 0

Question Number 195046 Answers: 2 Comments: 1

Question Number 195043 Answers: 2 Comments: 1

Question Number 195042 Answers: 1 Comments: 0

Question Number 195038 Answers: 0 Comments: 1

prove that x+y=(1/(x−y))

$${prove}\:{that}\:{x}+{y}=\frac{\mathrm{1}}{{x}−{y}} \\ $$

Question Number 195035 Answers: 2 Comments: 0

(√i)=?

$$\sqrt{{i}}=? \\ $$

Question Number 195033 Answers: 1 Comments: 0

any point is the function is not continous f(x)=(4x+8)^((ln45)/8) a) −8 b) −2 c) no one d) 5

$${any}\:{point}\:{is}\:{the}\:{function}\:{is} \\ $$$${not}\:{continous} \\ $$$${f}\left({x}\right)=\left(\mathrm{4}{x}+\mathrm{8}\right)^{\frac{{ln}\mathrm{45}}{\mathrm{8}}} \\ $$$$\left.{a}\left.\right)\:−\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\:−\mathrm{2} \\ $$$$\left.{c}\left.\right)\:{no}\:{one}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}\right)\:\mathrm{5} \\ $$

Question Number 195029 Answers: 1 Comments: 0

lim_(x→0^+ ) ((((√(x+x^2 )) −(√x))/( (√(3x)) ln (1+x))) ).

$$\:\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\frac{\sqrt{{x}+{x}^{\mathrm{2}} }\:−\sqrt{{x}}}{\:\sqrt{\mathrm{3}{x}}\:\mathrm{ln}\:\left(\mathrm{1}+{x}\right)}\:\right).\: \\ $$

Question Number 195027 Answers: 1 Comments: 2

a_3 x^3 −x^2 +a_1 x−7=0 is a cubic polynomial in x whose Roots are α , β , γ positive real numbers satisfying ((225α^2 )/(α^2 +7))=((144β^2 )/(β^2 +7))=((100γ^2 )/(γ^2 +7)) find (a_1 )

$${a}_{\mathrm{3}} {x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{a}_{\mathrm{1}} {x}−\mathrm{7}=\mathrm{0}\:{is}\:{a}\:{cubic}\:{polynomial}\:{in}\:{x} \\ $$$${whose}\:{Roots}\:{are}\:\alpha\:,\:\beta\:,\:\gamma\:{positive}\:{real}\:{numbers} \\ $$$${satisfying} \\ $$$$\frac{\mathrm{225}\alpha^{\mathrm{2}} }{\alpha^{\mathrm{2}} +\mathrm{7}}=\frac{\mathrm{144}\beta^{\mathrm{2}} }{\beta^{\mathrm{2}} +\mathrm{7}}=\frac{\mathrm{100}\gamma^{\mathrm{2}} }{\gamma^{\mathrm{2}} +\mathrm{7}} \\ $$$${find}\:\left({a}_{\mathrm{1}} \right) \\ $$

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