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AlgebraQuestion and Answers: Page 266

Question Number 84941 Answers: 2 Comments: 1

Question Number 84915 Answers: 1 Comments: 0

if x>0,y>0,z>0 show that ((x+y)/z)+((z+y)/( x))+((z+x)/y)≥6

$${if}\: \\ $$$${x}>\mathrm{0},{y}>\mathrm{0},{z}>\mathrm{0} \\ $$$${show}\:{that} \\ $$$$\frac{{x}+{y}}{{z}}+\frac{{z}+{y}}{\:{x}}+\frac{{z}+{x}}{{y}}\geqslant\mathrm{6}\:\: \\ $$

Question Number 84913 Answers: 2 Comments: 2

sin(π/(14)) sin((3π)/(14)) sin((5π)/(15))=?

$$ \\ $$$${sin}\frac{\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{5}\pi}{\mathrm{15}}=? \\ $$

Question Number 84891 Answers: 0 Comments: 0

Question Number 84871 Answers: 1 Comments: 1

If you know (((b^2 +c^2 −a^2 )/(2bc)))^2 +(((c^2 +a^2 −b^2 )/(2ca)))^2 +(((a^2 +b^2 −c^2 )/(2ab)))^2 =3, then what′s the value of ((b^2 +c^2 −a^2 )/(2bc))+((c^2 +a^2 −b^2 )/(2ac))+((a^2 +b^2 −c^2 )/(2ab))?

$$\mathrm{If}\:\mathrm{you}\:\mathrm{know} \\ $$$$\left(\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}\right)^{\mathrm{2}} +\left(\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ca}}\right)^{\mathrm{2}} +\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}\right)^{\mathrm{2}} =\mathrm{3}, \\ $$$$\mathrm{then}\:\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}+\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ac}}+\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}? \\ $$

Question Number 84835 Answers: 0 Comments: 1

Question Number 84820 Answers: 1 Comments: 0

Question Number 84792 Answers: 0 Comments: 0

a,b,c≥0 a+b+c=3 show that (a)^(1/3) +(b)^(1/3) +(c)^(1/3) ≥ab+bc+ca

$${a},{b},{c}\geqslant\mathrm{0} \\ $$$${a}+{b}+{c}=\mathrm{3} \\ $$$${show}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+\sqrt[{\mathrm{3}}]{{b}}\:+\sqrt[{\mathrm{3}}]{{c}}\geqslant{ab}+{bc}+{ca} \\ $$

Question Number 84783 Answers: 1 Comments: 6

Question Number 84782 Answers: 1 Comments: 8

Find the last three digits of 2019^(2019) .

$${Find}\:{the}\:{last}\:{three}\:{digits}\:{of}\:\mathrm{2019}^{\mathrm{2019}} . \\ $$

Question Number 84770 Answers: 2 Comments: 1

x^2 +y^2 = 30 (1/x)+(1/y) = 2 find the solution x & y ?

$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{30}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}\:=\:\mathrm{2}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{x}\:\&\:\mathrm{y}\:? \\ $$

Question Number 84728 Answers: 0 Comments: 8

y=x[x[x]] with x∈R^+ find the range of function and solve x[x[x]]=150.

$${y}={x}\left[{x}\left[{x}\right]\right]\:{with}\:{x}\in{R}^{+} \\ $$$${find}\:{the}\:{range}\:{of}\:{function} \\ $$$${and}\:{solve}\:{x}\left[{x}\left[{x}\right]\right]=\mathrm{150}. \\ $$

Question Number 84785 Answers: 1 Comments: 2

at what time is the short clock and long hour hand form an angle of 180 degrees?

$$\mathrm{at}\:\mathrm{what}\:\mathrm{time}\:\mathrm{is}\:\mathrm{the}\:\mathrm{short}\:\mathrm{clock}\: \\ $$$$\mathrm{and}\:\mathrm{long}\:\mathrm{hour}\:\mathrm{hand}\:\mathrm{form}\:\mathrm{an}\: \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{180}\:\mathrm{degrees}? \\ $$

Question Number 84711 Answers: 0 Comments: 2

Question Number 84632 Answers: 0 Comments: 0

Question Number 84588 Answers: 2 Comments: 0

if x − (1/x) = 9 x^3 −(1/x^3 ) = ?

$$\mathrm{if}\:\mathrm{x}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{9} \\ $$$$\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 84528 Answers: 0 Comments: 3

1=2

$$\mathrm{1}=\mathrm{2} \\ $$

Question Number 84515 Answers: 1 Comments: 0

Q.solve x^3 −x=x!

$${Q}.{solve} \\ $$$${x}^{\mathrm{3}} −{x}={x}! \\ $$

Question Number 84430 Answers: 0 Comments: 4

Question Number 84420 Answers: 1 Comments: 2

Question Number 84404 Answers: 0 Comments: 1

(x^2 −2)(x^2 −4)(x^2 −6)...(x^2 −2020)=1 x=?

$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{6}\right)...\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2020}\right)=\mathrm{1} \\ $$$$\mathrm{x}=? \\ $$

Question Number 84394 Answers: 0 Comments: 2

find the solution ((2x)/(x−2)) ≤ ∣x−3∣

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution} \\ $$$$\frac{\mathrm{2x}}{\mathrm{x}−\mathrm{2}}\:\leqslant\:\mid\mathrm{x}−\mathrm{3}\mid\: \\ $$

Question Number 84393 Answers: 0 Comments: 0

if x^x .y^y .z^z =x^y .y^z .z^x =x^z .y^x .z^y such that x, y and z are positive intigers greater than 1 ,what is the value of xyz and x+y+z ?

$${if}\:{x}^{{x}} .{y}^{{y}} .{z}^{{z}} ={x}^{{y}} .{y}^{{z}} .{z}^{{x}} ={x}^{{z}} .{y}^{{x}} .{z}^{{y}} \:{such}\:{that}\:{x},\:{y}\:{and}\:{z}\: \\ $$$${are}\:{positive}\:{intigers}\:{greater}\:{than}\:\mathrm{1} \\ $$$$,{what}\:{is}\:{the}\:{value}\:{of}\:{xyz}\:{and}\:{x}+{y}+{z}\:? \\ $$

Question Number 84384 Answers: 0 Comments: 3

[x]^x =2(√2) , ∀x>0

$$\left[{x}\right]^{{x}} =\mathrm{2}\sqrt{\mathrm{2}}\:\:,\:\forall{x}>\mathrm{0} \\ $$

Question Number 84370 Answers: 2 Comments: 0

1.) ∣x∣ +∣x+2∣ <5 2.) ∣x∣ +∣x+2∣ + ∣2−x∣ ≤8

$$\left.\mathrm{1}.\right)\:\mid{x}\mid\:+\mid{x}+\mathrm{2}\mid\:<\mathrm{5} \\ $$$$\left.\mathrm{2}.\right)\:\mid{x}\mid\:+\mid{x}+\mathrm{2}\mid\:+\:\mid\mathrm{2}−{x}\mid\:\leqslant\mathrm{8} \\ $$

Question Number 84328 Answers: 0 Comments: 0

(3/7)×(1/2)ln[((u−1)/(u+1))]−(1/2)ln[u^2 −1]

$$\frac{\mathrm{3}}{\mathrm{7}}×\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\left[\frac{\mathrm{u}−\mathrm{1}}{\mathrm{u}+\mathrm{1}}\right]−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\left[\mathrm{u}^{\mathrm{2}} −\mathrm{1}\right] \\ $$

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