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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

Question Number 192763 Answers: 1 Comments: 0

Prove that: sin A + sin B + sin C > 2 (A,B,C ∈ (π/2))

$${Prove}\:{that}: \\ $$$${sin}\:{A}\:+\:{sin}\:{B}\:+\:{sin}\:{C}\:>\:\mathrm{2} \\ $$$$\left({A},{B},{C}\:\in\:\frac{\pi}{\mathrm{2}}\right) \\ $$

Question Number 192758 Answers: 3 Comments: 0

what is the value of dy/dx if y = cot^(−1) [(((√(1+sinx))+(√(1−sinx)))/( (√(1+sinx))−(√(1−sinx))))]; x∈(0,(π/2)) please give complete explanation that why can we not take [sinx/2−cosx/2]^2 = 1−sinx

$${what}\:{is}\:{the}\:{value}\:{of}\:{dy}/{dx}\:{if} \\ $$$${y}\:=\:{cot}^{−\mathrm{1}} \left[\frac{\sqrt{\mathrm{1}+{sinx}}+\sqrt{\mathrm{1}−{sinx}}}{\:\sqrt{\mathrm{1}+{sinx}}−\sqrt{\mathrm{1}−{sinx}}}\right];\:{x}\in\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right) \\ $$$${please}\:{give}\:{complete}\:{explanation}\:{that} \\ $$$${why}\:{can}\:{we}\:{not}\:{take} \\ $$$$\left[{sinx}/\mathrm{2}−{cosx}/\mathrm{2}\right]^{\mathrm{2}} \:=\:\mathrm{1}−{sinx} \\ $$

Question Number 192756 Answers: 1 Comments: 1

Question Number 192777 Answers: 0 Comments: 2

(√(x^2 +ax−1))−(√(x^2 +bx−1))=(√a)−(√b) find x .

$$\sqrt{{x}^{\mathrm{2}} +{ax}−\mathrm{1}}−\sqrt{{x}^{\mathrm{2}} +{bx}−\mathrm{1}}=\sqrt{{a}}−\sqrt{{b}} \\ $$$${find}\:{x}\:. \\ $$

Question Number 192746 Answers: 1 Comments: 0

Let G be the group ({1, ı, −1, −ı}, ∙) and let H ≤ (+_− 1, ∙), show that θ:G→H is an Isomorphism. Hello!

$$\mathrm{Let}\:\mathrm{G}\:\mathrm{be}\:\mathrm{the}\:\mathrm{group}\:\left(\left\{\mathrm{1},\:\imath,\:−\mathrm{1},\:−\imath\right\},\:\centerdot\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{H}\:\leqslant\:\left(\underset{−} {+}\mathrm{1},\:\centerdot\right),\:\mathrm{show}\:\mathrm{that} \\ $$$$\theta:\mathrm{G}\rightarrow\mathrm{H}\:\mathrm{is}\:\mathrm{an}\:\mathrm{Isomorphism}. \\ $$$$ \\ $$$$\mathrm{Hello}! \\ $$

Question Number 192743 Answers: 1 Comments: 0

Calculate: I=∫_0 ^( 4) (∫_(x−4) ^( x−2) e^((x+y)/(x−y)) dy)dx

$${Calculate}: \\ $$$${I}=\int_{\mathrm{0}} ^{\:\mathrm{4}} \left(\int_{{x}−\mathrm{4}} ^{\:{x}−\mathrm{2}} {e}^{\frac{{x}+{y}}{{x}−{y}}} {dy}\right){dx} \\ $$

Question Number 192738 Answers: 2 Comments: 0

Find the supremum and infimum of each of the following sequence a) {((n−1)/(2n))} b) {(((−)^n n)/(2n+1))} c){((1+(−)^n )/3)} d) {sin((nπ)/2)} e) {(1/n) − sin((nπ)/2)} f) {(1+(1/(2n)))cos((nπ)/3)} Help!

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{supremum}\:\mathrm{and}\:\mathrm{infimum} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$ \\ $$$$\left.\mathrm{a}\left.\right)\left.\:\left\{\frac{\mathrm{n}−\mathrm{1}}{\mathrm{2n}}\right\}\:\:\:\:\mathrm{b}\right)\:\left\{\frac{\left(−\right)^{\mathrm{n}} \mathrm{n}}{\mathrm{2n}+\mathrm{1}}\right\}\:\:\:\:\mathrm{c}\right)\left\{\frac{\mathrm{1}+\left(−\right)^{\mathrm{n}} }{\mathrm{3}}\right\} \\ $$$$ \\ $$$$\left.\mathrm{d}\left.\right)\:\left\{\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\}\:\:\:\:\mathrm{e}\right)\:\left\{\frac{\mathrm{1}}{\mathrm{n}}\:−\:\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\} \\ $$$$ \\ $$$$\left.\mathrm{f}\right)\:\left\{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2n}}\right)\mathrm{cos}\frac{\mathrm{n}\pi}{\mathrm{3}}\right\} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192737 Answers: 1 Comments: 0

Prove that the sequence {a_n } is null when {a_n } is given by ((n^3 +2n^2 −1)/(n^4 −n^2 +2)) Help!

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{null} \\ $$$$\mathrm{when}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{n}^{\mathrm{3}} +\mathrm{2n}^{\mathrm{2}} −\mathrm{1}}{\mathrm{n}^{\mathrm{4}} −\mathrm{n}^{\mathrm{2}} +\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192733 Answers: 1 Comments: 0