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Question Number 153340 Answers: 1 Comments: 0

Solve .. x , y , z ∈ R^( +) & x+ y= z K := Min_ ((( x^( 4) + y^( 4) + z^( 4) )/(x^( 2) y^( 2) )) ) = ? ■ Source : Elementary Olympid Book m.n

$$ \\ $$$$\:\:\:\:\:\mathrm{Solve}\:.. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:,\:\mathrm{z}\:\in\:\mathbb{R}^{\:+} \:\&\:\:\mathrm{x}+\:\mathrm{y}=\:\mathrm{z} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{K}\::=\:\mathrm{Min}_{\:} \:\left(\frac{\:\mathrm{x}^{\:\mathrm{4}} \:+\:\mathrm{y}^{\:\mathrm{4}} +\:\mathrm{z}^{\:\mathrm{4}} }{\mathrm{x}^{\:\mathrm{2}} \mathrm{y}^{\:\mathrm{2}} }\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{Source}\::\:\:\mathrm{Elementary}\:\mathrm{Olympid}\:\mathrm{Book}\:\:{m}.{n} \\ $$$$ \\ $$

Question Number 153339 Answers: 2 Comments: 0

((x−1)/x)+((x−2)/x)+((x−3)/x)+…+(1/x)=3 x=? ∵∴∵∴∵ Easy question∴∵∴∵∴∵

$$\:\:\frac{{x}−\mathrm{1}}{{x}}+\frac{{x}−\mathrm{2}}{{x}}+\frac{{x}−\mathrm{3}}{{x}}+\ldots+\frac{\mathrm{1}}{{x}}=\mathrm{3}\:\:\:\:{x}=? \\ $$$$\because\therefore\because\therefore\because\:\:{Easy}\:{question}\therefore\because\therefore\because\therefore\because \\ $$

Question Number 153335 Answers: 0 Comments: 0

Question Number 153312 Answers: 0 Comments: 3

Question Number 153263 Answers: 0 Comments: 0

Question Number 153257 Answers: 2 Comments: 0

Find set of k value so that ∣x∣ + ∣x−1∣ + ∣x−4∣ = k a. has one solution b. has two solutions c. has many solutions d. has no solution

$${Find}\:\:{set}\:\:{of}\:\:{k}\:\:{value}\:\:{so}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\mid{x}\mid\:+\:\mid{x}−\mathrm{1}\mid\:+\:\mid{x}−\mathrm{4}\mid\:=\:{k} \\ $$$${a}.\:{has}\:\:{one}\:\:{solution} \\ $$$${b}.\:{has}\:\:{two}\:\:{solutions} \\ $$$${c}.\:{has}\:\:{many}\:\:{solutions} \\ $$$${d}.\:{has}\:\:{no}\:\:{solution} \\ $$

Question Number 153256 Answers: 0 Comments: 1

Question Number 153252 Answers: 1 Comments: 0

Question Number 153249 Answers: 1 Comments: 0

Question Number 153245 Answers: 2 Comments: 0

{ ((x^3 −3x^2 y=30)),((y^3 −3xy^2 =10)) :} (x,y)=?

$$\:\:\begin{cases}{{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}=\mathrm{30}}\\{{y}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} =\mathrm{10}}\end{cases} \\ $$$$\:\left({x},{y}\right)=? \\ $$

Question Number 153239 Answers: 1 Comments: 0

Question Number 153227 Answers: 2 Comments: 0

let D= [((v 5)),(((1/3) m)) ] find number (v) and (m) such that D^2 =5I (I=identity matrix)

$${let}\:{D}=\begin{bmatrix}{{v}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}}\\{\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\:\:{m}}\end{bmatrix}\:{find}\:{number}\:\left({v}\right)\:{and} \\ $$$$\left({m}\right)\:{such}\:{that}\:{D}^{\mathrm{2}} =\mathrm{5}{I}\:\:\:\:\:\left({I}={identity}\:{matrix}\right) \\ $$

Question Number 153226 Answers: 1 Comments: 4

Question Number 153220 Answers: 1 Comments: 0

in how many ways can the number n be written as a sum of three positive integers if representations differing in the order of the terms are considered to be different?

$$\: \\ $$$$\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{number}\:\: \\ $$$$\:{n}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{positive}\:\: \\ $$$$\:\mathrm{integers}\:\mathrm{if}\:\mathrm{representations}\:\mathrm{differing}\:\: \\ $$$$\:\mathrm{in}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{considered}\:\: \\ $$$$\:\mathrm{to}\:\mathrm{be}\:\mathrm{different}?\:\: \\ $$$$\: \\ $$

Question Number 153214 Answers: 1 Comments: 0

let a,b∈N^∗ a∗b=a+b+ab a^((n)) =a^((n−1)) ∗a explicite a^((n)) en fonction de a

$$\boldsymbol{{let}}\:\boldsymbol{{a}},\boldsymbol{{b}}\in\mathbb{N}^{\ast} \: \\ $$$$\:\boldsymbol{{a}}\ast\boldsymbol{{b}}=\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{ab}} \\ $$$$\boldsymbol{{a}}^{\left(\boldsymbol{{n}}\right)} =\boldsymbol{{a}}^{\left(\boldsymbol{{n}}−\mathrm{1}\right)} \ast\boldsymbol{{a}} \\ $$$$\boldsymbol{{explicite}}\:\boldsymbol{{a}}^{\left(\boldsymbol{{n}}\right)} \:\boldsymbol{{en}}\:\boldsymbol{{fonction}}\:\boldsymbol{{de}}\:\boldsymbol{{a}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 153216 Answers: 0 Comments: 1

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Question Number 153212 Answers: 0 Comments: 0

∫_(−∞) ^( ∞) (( tan(x).Arctanh(cos(x)))/x)dx=?

$$ \\ $$$$\:\:\int_{−\infty} ^{\:\infty} \frac{\:{tan}\left({x}\right).{Arctanh}\left({cos}\left({x}\right)\right)}{{x}}{dx}=? \\ $$$$ \\ $$

Question Number 153208 Answers: 0 Comments: 0

Question Number 153201 Answers: 0 Comments: 0

Question Number 153200 Answers: 0 Comments: 0

∫_0 ^(e−1) ∫_0 ^(e−x−1) ∫_0 ^(x+y+e) ((ln(z−x−y))/((x−e)(x+y−e)))dxdydz=?

$$\int_{\mathrm{0}} ^{{e}−\mathrm{1}} \int_{\mathrm{0}} ^{{e}−{x}−\mathrm{1}} \int_{\mathrm{0}} ^{{x}+{y}+{e}} \frac{{ln}\left({z}−{x}−{y}\right)}{\left({x}−{e}\right)\left({x}+{y}−{e}\right)}{dxdydz}=? \\ $$

Question Number 153203 Answers: 2 Comments: 0

Question Number 153194 Answers: 0 Comments: 0

Question Number 153189 Answers: 2 Comments: 0

Question Number 153181 Answers: 0 Comments: 2

Question Number 153182 Answers: 0 Comments: 2

Question Number 153174 Answers: 0 Comments: 1

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