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AllQuestion and Answers: Page 278

Question Number 192862 Answers: 1 Comments: 0

Solve for x x^3 −115x+150=0

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{115}{x}+\mathrm{150}=\mathrm{0} \\ $$

Question Number 192858 Answers: 1 Comments: 0

∫_(4x) ^( x^3 ) (√((√t)+t^(1/3) ))dt

$$\int_{\mathrm{4}{x}} ^{\:{x}^{\mathrm{3}} } \sqrt{\sqrt{{t}}+{t}^{\mathrm{1}/\mathrm{3}} }{dt} \\ $$

Question Number 192856 Answers: 2 Comments: 0

if a+b+c +d = 63 and a,b,c,d ∈ N find the maximum value of ab+bc+cd = ?

$$\:{if}\:{a}+{b}+{c}\:+{d}\:\:=\:\mathrm{63}\:{and}\:{a},{b},{c},{d}\:\in\:\mathbb{N}\:{find}\: \\ $$$$\:\:\:{the}\:{maximum}\:{value}\:{of}\:{ab}+{bc}+{cd}\:=\:? \\ $$

Question Number 192855 Answers: 2 Comments: 0

Question Number 192852 Answers: 2 Comments: 2

find the domain of thefunction f(x) = (1/( (√(x^2 −{x}^2 )))) where {.} is the fractional part function.

$$ \\ $$$${find}\:{the}\:{domain}\:{of}\:{thefunction} \\ $$$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\left\{{x}\right\}^{\mathrm{2}} }}\:\:\:\:\:{where}\:\left\{.\right\}\:{is}\:{the}\:{fractional}\:{part}\:{function}. \\ $$

Question Number 192851 Answers: 0 Comments: 1

Solve: ((log_(a^2 (√x)) a)/(log_(2x) a)) + log_(ax) a . log_(1/a) 2x = 0

$$\mathrm{Solve}: \\ $$$$\frac{\mathrm{log}_{{a}^{\mathrm{2}} \sqrt{{x}}} \:{a}}{\mathrm{log}_{\mathrm{2}{x}} \:{a}}\:+\:\mathrm{log}_{{ax}} \:{a}\:.\:\mathrm{log}_{\frac{\mathrm{1}}{{a}}} \:\mathrm{2}{x}\:=\:\mathrm{0} \\ $$

Question Number 192849 Answers: 0 Comments: 0

Question Number 192848 Answers: 0 Comments: 0

Question Number 192846 Answers: 1 Comments: 0

lim_(h→0) ((3h)/( ((3h+x))^(1/5) −(x)^(1/5) ))=?

$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{h}}{\:\sqrt[{\mathrm{5}}]{\mathrm{3}{h}+{x}}−\sqrt[{\mathrm{5}}]{{x}}}=? \\ $$

Question Number 192841 Answers: 1 Comments: 0

Question Number 192839 Answers: 2 Comments: 0

Question Number 192836 Answers: 0 Comments: 1

Question Number 192828 Answers: 2 Comments: 1

Question Number 192819 Answers: 2 Comments: 0

Question Number 192811 Answers: 1 Comments: 0

Question Number 192816 Answers: 0 Comments: 0

Question Number 192814 Answers: 0 Comments: 0

Question Number 192803 Answers: 1 Comments: 1

Question Number 192797 Answers: 1 Comments: 0

If x & y are both positive integers then then show if it possiple that x^2 +y+1 & y^2 + 4x + 3 be both perfect squares simultaneously.

$$\boldsymbol{{If}}\:\boldsymbol{{x}}\:\&\:\boldsymbol{{y}}\:\boldsymbol{{are}}\:\boldsymbol{{both}}\:\boldsymbol{{positive}}\:\boldsymbol{{integers}}\:\boldsymbol{{then}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{show}}\:\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{possiple}}\:\boldsymbol{{that}}\:\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}+\mathrm{1}\:\&\:\boldsymbol{{y}}^{\mathrm{2}} \:+\:\mathrm{4}\boldsymbol{{x}}\:+\:\mathrm{3}\:\boldsymbol{{be}}\:\boldsymbol{{both}}\: \\ $$$$\boldsymbol{{perfect}}\:\boldsymbol{{squares}}\:\boldsymbol{{simultaneously}}. \\ $$

Question Number 192793 Answers: 2 Comments: 0

x^4 +x^3 +x^2 +x+1=y^2 where y is positive integer number then find the positive integal values of (x) for which that holds

$$\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{x}}+\mathrm{1}=\boldsymbol{{y}}^{\mathrm{2}} \:\boldsymbol{{where}}\:\boldsymbol{{y}}\:\boldsymbol{{is}}\:\boldsymbol{{positive}}\:\boldsymbol{{integer}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{positive}}\:\boldsymbol{{integal}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\left(\boldsymbol{{x}}\right) \\ $$$$\boldsymbol{{for}}\:\boldsymbol{{which}}\:\boldsymbol{{that}}\:\boldsymbol{{holds}} \\ $$

Question Number 192791 Answers: 1 Comments: 0

If n is a positive integer, prove that 2^n Γ(n+(1/2)) = 1.3.5...(2n−1)(√π). Help!

$$\mathrm{If}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{2}^{\mathrm{n}} \Gamma\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\:=\:\mathrm{1}.\mathrm{3}.\mathrm{5}...\left(\mathrm{2n}−\mathrm{1}\right)\sqrt{\pi}. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192786 Answers: 1 Comments: 0

N=<aabb>∈N & N is perfect square find N ?

$${N}=<{aabb}>\in\mathbb{N}\:\:\&\:\:{N}\:\:{is}\:\:{perfect}\:{square} \\ $$$${find}\:\:{N}\:\:? \\ $$$$ \\ $$

Question Number 192780 Answers: 1 Comments: 1

Question Number 192770 Answers: 1 Comments: 4

Question Number 192766 Answers: 0 Comments: 0

if π/2<x<π and (√(1+sin x/1−sin x= ksec x ,then k=))

$${if}\:\pi/\mathrm{2}<{x}<\pi\:{and}\:\sqrt{\mathrm{1}+\mathrm{sin}\:{x}/\mathrm{1}−\mathrm{sin}\:{x}=\:{k}\mathrm{sec}\:{x}\:,{then}\:{k}=} \\ $$

Question Number 192765 Answers: 1 Comments: 0

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