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AllQuestion and Answers: Page 556

Question Number 154330 Answers: 1 Comments: 0

Question Number 154321 Answers: 2 Comments: 0

Question Number 154316 Answers: 1 Comments: 0

If x^3 + (1/y^3 ) = y^3 + (1/z^3 ) = 1 Find (xyz)^(2025) - 1 = ?

$$\mathrm{If}\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{3}} }\:=\:\mathrm{y}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{1} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{xyz}\right)^{\mathrm{2025}} \:-\:\mathrm{1}\:=\:? \\ $$

Question Number 154320 Answers: 1 Comments: 0

if a;b;c>0 and ab+bc+ca=2 then: Σ_(cyc) ((a(b^4 + c^4 ))/(b^3 + b^2 c + bc^2 + c^3 )) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$

Question Number 154318 Answers: 1 Comments: 0

Question Number 154309 Answers: 1 Comments: 0

Question Number 154306 Answers: 0 Comments: 1

Question Number 154303 Answers: 1 Comments: 1

Solve in R ((z^9 - 81z - 62)/z^3 ) = 18 ((3z + 2))^(1/3)

$$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{z}^{\mathrm{9}} \:-\:\mathrm{81z}\:-\:\mathrm{62}}{\mathrm{z}^{\mathrm{3}} }\:=\:\mathrm{18}\:\sqrt[{\mathrm{3}}]{\mathrm{3z}\:+\:\mathrm{2}} \\ $$

Question Number 154301 Answers: 1 Comments: 0

of the integers 101 to 400 (including 101 and 400 themselves) how many are not divisible by 3 or 5?

$$\mathrm{of}\:\mathrm{the}\:\mathrm{integers}\:\mathrm{101}\:\mathrm{to}\:\mathrm{400}\:\left(\mathrm{including}\:\mathrm{101}\:\mathrm{and}\:\mathrm{400}\:\right. \\ $$$$\left.\mathrm{themselves}\right)\:\mathrm{how}\:\mathrm{many}\:\mathrm{are}\:\mathrm{not}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{or}\:\mathrm{5}? \\ $$

Question Number 154296 Answers: 0 Comments: 0

Question Number 154292 Answers: 2 Comments: 0

Question Number 154291 Answers: 2 Comments: 0

Among the integers 101−400,how many numbers are divisible by 3 but no divisible by 5 or 7

$$\mathrm{Among}\:\mathrm{the}\:\mathrm{integers}\:\mathrm{101}−\mathrm{400},\mathrm{how}\:\mathrm{many}\:\mathrm{numbers} \\ $$$$\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{but}\:\mathrm{no}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5}\:\mathrm{or}\:\mathrm{7} \\ $$

Question Number 154289 Answers: 0 Comments: 0

solve ∫4x^(5x) dx=?

$${solve}\: \\ $$$$\int\mathrm{4}{x}^{\mathrm{5}{x}} {dx}=? \\ $$

Question Number 154287 Answers: 0 Comments: 0

Question Number 154285 Answers: 0 Comments: 0

Question Number 154286 Answers: 1 Comments: 5

h = ((52−47i))^(1/3) +((52+47i))^(1/3) find h^2 .

$$\:{h}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{52}−\mathrm{47}{i}}\:+\sqrt[{\mathrm{3}}]{\mathrm{52}+\mathrm{47}{i}}\: \\ $$$$\:{find}\:{h}^{\mathrm{2}} . \\ $$

Question Number 154281 Answers: 0 Comments: 0

∫_1 ^3 ⌊x−3⌋dx

$$\int_{\mathrm{1}} ^{\mathrm{3}} \lfloor{x}−\mathrm{3}\rfloor{dx} \\ $$

Question Number 154280 Answers: 0 Comments: 0

∫_0 ^( 1) ∫_0 ^( z^2 ) ∫_0 ^( 3) y cos (z^5 )dxdydz =?

$$\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:{z}^{\mathrm{2}} } \int_{\mathrm{0}} ^{\:\mathrm{3}} {y}\:\mathrm{cos}\:\left({z}^{\mathrm{5}} \right){dxdydz}\:=? \\ $$

Question Number 154275 Answers: 0 Comments: 1

Question Number 154274 Answers: 0 Comments: 1

Solve the equation: x^2 ∙2^x (x^4 ∙4^x + 3∙15^x ) = 125^x - 27^x

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{x}^{\mathrm{2}} \centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \left(\mathrm{x}^{\mathrm{4}} \centerdot\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{3}\centerdot\mathrm{15}^{\boldsymbol{\mathrm{x}}} \right)\:=\:\mathrm{125}^{\boldsymbol{\mathrm{x}}} \:-\:\mathrm{27}^{\boldsymbol{\mathrm{x}}} \\ $$

Question Number 154273 Answers: 1 Comments: 0

Question Number 154270 Answers: 0 Comments: 0

Question Number 154268 Answers: 0 Comments: 3

Question Number 154267 Answers: 0 Comments: 0

if x;y;z>0 and xy+yz+zx=3xyz then: (Σ_(cyc) (1/(x+y)))(Σ_(cyc) (1/(2x+y+z))) ≤ (9/8)

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\mathrm{and}\:\mathrm{xy}+\mathrm{yz}+\mathrm{zx}=\mathrm{3xyz}\:\:\mathrm{then}: \\ $$$$\left(\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{1}}{\mathrm{x}+\mathrm{y}}\right)\left(\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{1}}{\mathrm{2x}+\mathrm{y}+\mathrm{z}}\right)\:\leqslant\:\frac{\mathrm{9}}{\mathrm{8}} \\ $$

Question Number 154262 Answers: 1 Comments: 0

Question Number 154258 Answers: 1 Comments: 0

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