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AlgebraQuestion and Answers: Page 264

Question Number 86903    Answers: 0   Comments: 0

Question Number 86825    Answers: 1   Comments: 1

a^3 +(1/a^3 )=18 a^4 +(1/a^4 )=?

$${a}^{\mathrm{3}} +\frac{\mathrm{1}}{{a}^{\mathrm{3}} }=\mathrm{18} \\ $$$${a}^{\mathrm{4}} +\frac{\mathrm{1}}{{a}^{\mathrm{4}} }=? \\ $$

Question Number 86779    Answers: 1   Comments: 0

ssolve 1)x−[x]≥0 2)x−[x]≤0 3)x+[x]≥0 4)x+[x]≤0

$${ssolve} \\ $$$$\left.\mathrm{1}\right){x}−\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{2}\right){x}−\left[{x}\right]\leqslant\mathrm{0} \\ $$$$\left.\mathrm{3}\right){x}+\left[{x}\right]\geqslant\mathrm{0} \\ $$$$\left.\mathrm{4}\right){x}+\left[{x}\right]\leqslant\mathrm{0}\: \\ $$

Question Number 86741    Answers: 1   Comments: 4

{ ((x+10y+50z=500)),((x+y+z=100)) :} find x,y,z

$$\begin{cases}{{x}+\mathrm{10}{y}+\mathrm{50}{z}=\mathrm{500}}\\{{x}+{y}+{z}=\mathrm{100}}\end{cases} \\ $$$$ \\ $$$${find}\:{x},{y},{z} \\ $$

Question Number 86737    Answers: 2   Comments: 4

prove that 1/cos2x+cosx+1=((sin((5x)/2))/(2sin(x/2)))+(1/2) 2/((cos(x)+isin(x)−1)/(cos(x)+isin(x)+1))=−i tan(x) 3/((cos(5x)+isin(5x)+1)/(cos(5x)−isin(x)+1))=cos(5x)+isin(5x)

$${prove}\:{that} \\ $$$$\mathrm{1}/{cos}\mathrm{2}{x}+{cosx}+\mathrm{1}=\frac{{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}}{\mathrm{2}{sin}\frac{{x}}{\mathrm{2}}}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{2}/\frac{{cos}\left({x}\right)+{isin}\left({x}\right)−\mathrm{1}}{{cos}\left({x}\right)+{isin}\left({x}\right)+\mathrm{1}}=−{i}\:{tan}\left({x}\right) \\ $$$$ \\ $$$$\mathrm{3}/\frac{{cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right)+\mathrm{1}}{{cos}\left(\mathrm{5}{x}\right)−{isin}\left({x}\right)+\mathrm{1}}={cos}\left(\mathrm{5}{x}\right)+{isin}\left(\mathrm{5}{x}\right) \\ $$

Question Number 86723    Answers: 0   Comments: 1

Question Number 86610    Answers: 0   Comments: 4

Question Number 86602    Answers: 0   Comments: 0

Question Number 86586    Answers: 1   Comments: 4

Question Number 86541    Answers: 0   Comments: 1

Question Number 86426    Answers: 2   Comments: 0

solve in R x^3 −5=[x]

$${solve}\:{in}\:{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{5}=\left[{x}\right] \\ $$

Question Number 86396    Answers: 0   Comments: 0

Question Number 86298    Answers: 0   Comments: 5

let x^x^x^⋰ =2 x^2 =2 x=±(√2) then let x^x^x^⋰ =4 x^4 =4 x=±(4)^(1/4) =±(√2) so we had prove 2=4 right?

$${let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{2} \\ $$$${x}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}=\pm\sqrt{\mathrm{2}} \\ $$$${then}\:{let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{4} \\ $$$${x}^{\mathrm{4}} =\mathrm{4} \\ $$$${x}=\pm\sqrt[{\mathrm{4}}]{\mathrm{4}}=\pm\sqrt{\mathrm{2}} \\ $$$${so}\:{we}\:{had}\:{prove}\:\mathrm{2}=\mathrm{4}\:{right}? \\ $$

Question Number 86230    Answers: 1   Comments: 0

is (−1)^(m/n) =((((−1 )^m ))^(1/n) ) or =(((−1))^(1/n) )^m or both of them are fault and why ?

$${is}\:\:\left(−\mathrm{1}\right)^{\frac{{m}}{{n}}} \:=\left(\sqrt[{{n}}]{\left(−\mathrm{1}\:\right)^{{m}} }\right)\:{or}\:=\left(\sqrt[{{n}}]{−\mathrm{1}}\right)^{{m}} \\ $$$${or}\:{both}\:{of}\:{them}\:{are}\:{fault}\:{and}\:{why}\:? \\ $$

Question Number 86206    Answers: 0   Comments: 3

1.line:y=−x+4 ,meets : xy=1 at:A,B. ⇒ S_(OA^△ B) =? (O=origin of cordinates) 2.find :center area of region bonded by corve: (√(x/a))+(√(y/b))=1,and x,y axes. (a≠b)∈R^+

$$\mathrm{1}.\mathrm{line}:\boldsymbol{\mathrm{y}}=−\boldsymbol{\mathrm{x}}+\mathrm{4}\:\:,\mathrm{meets}\::\:\boldsymbol{\mathrm{xy}}=\mathrm{1}\:\mathrm{at}:\boldsymbol{\mathrm{A}},\boldsymbol{\mathrm{B}}. \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\mathrm{S}_{\mathrm{O}\overset{\bigtriangleup} {\mathrm{A}B}} =?\:\left(\mathrm{O}=\mathrm{origin}\:\mathrm{of}\:\mathrm{cordinates}\right) \\ $$$$\mathrm{2}.\mathrm{find}\::\mathrm{center}\:\mathrm{area}\:\mathrm{of}\:\mathrm{region}\:\mathrm{bonded}\:\mathrm{by} \\ $$$$\mathrm{corve}:\:\:\sqrt{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{a}}}}+\sqrt{\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{b}}}}=\mathrm{1},\mathrm{and}\:\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\:\mathrm{axes}. \\ $$$$\left(\boldsymbol{\mathrm{a}}\neq\boldsymbol{\mathrm{b}}\right)\in\boldsymbol{\mathrm{R}}^{+} \\ $$

Question Number 86141    Answers: 0   Comments: 5

A number n leaves a remainder of 22 when divided by 24 and remainder 30 when divided by 33. Find the least possible value of n

$$\mathrm{A}\:\mathrm{number}\:\mathrm{n}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{22}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{remainder}\:\:\mathrm{30}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{33}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{n} \\ $$

Question Number 86085    Answers: 1   Comments: 4

If X^2 +Y^2 =10 XY=5 Find (X^2 −Y^2 )

$$\mathrm{If}\:\mathrm{X}^{\mathrm{2}} +\mathrm{Y}^{\mathrm{2}} =\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{XY}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{X}^{\mathrm{2}} −\mathrm{Y}^{\mathrm{2}} \right) \\ $$

Question Number 86042    Answers: 3   Comments: 0

solve: ⌊ (√x) ⌋=⌊(x/2)⌋

$${solve}:\:\:\lfloor\:\sqrt{{x}}\:\rfloor=\lfloor\frac{{x}}{\mathrm{2}}\rfloor \\ $$

Question Number 86009    Answers: 1   Comments: 0

solve in R :[(x/2)]+[((2x)/3)]−x=0

$${solve}\:{in}\:{R}\::\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]−{x}=\mathrm{0} \\ $$

Question Number 86000    Answers: 1   Comments: 0

solve the equation x^(1/3) =4

$${solve}\:{the}\:{equation}\:\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} =\mathrm{4} \\ $$

Question Number 85930    Answers: 0   Comments: 1

Question Number 85902    Answers: 1   Comments: 15

find the coefficients of x^2 and x^3 terms in the expansion of (1+x)(1+2x)^2 (1+3x)^3 ...(1+100x)^(100)

$${find}\:{the}\:{coefficients}\:{of}\:{x}^{\mathrm{2}} \:{and}\:{x}^{\mathrm{3}} \: \\ $$$${terms}\:{in}\:{the}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} \left(\mathrm{1}+\mathrm{3}{x}\right)^{\mathrm{3}} ...\left(\mathrm{1}+\mathrm{100}{x}\right)^{\mathrm{100}} \\ $$

Question Number 85871    Answers: 0   Comments: 3

Question Number 85864    Answers: 1   Comments: 0

simplify the expression (√(6+2(√(8(√3)−10)))) − (√(7−(√3))) in the form (√((√a)+b)) ?

$${simplify}\:{the}\:{expression} \\ $$$$\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{8}\sqrt{\mathrm{3}}−\mathrm{10}}}\:−\:\sqrt{\mathrm{7}−\sqrt{\mathrm{3}}}\:\:{in} \\ $$$${the}\:{form}\:\sqrt{\sqrt{{a}}+{b}}\:? \\ $$

Question Number 85854    Answers: 0   Comments: 2

If x,y,z ∈ R satisfy the equation x^4 + y^4 + z^4 = 4xyz −1 find minimum value of x + y + z

$$\mathrm{If}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:+\:\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{4xyz}\:−\mathrm{1}\: \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\: \\ $$

Question Number 85822    Answers: 2   Comments: 1

how to solve ((x−1))^(1/(3 )) + ((x−3))^(1/(3 )) + ((x−5))^(1/(3 )) = 0

$$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{3}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{5}}\:=\:\mathrm{0}\: \\ $$

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