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Question Number 20366 Answers: 1 Comments: 0

tan^2 x+2tan x (sin y+cos y)+2=0 Find x,y .

$$\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{2tan}\:{x}\:\left(\mathrm{sin}\:{y}+\mathrm{cos}\:{y}\right)+\mathrm{2}=\mathrm{0} \\ $$$${Find}\:{x},{y}\:. \\ $$

Question Number 20298 Answers: 1 Comments: 0

Question Number 20297 Answers: 1 Comments: 0

Prove that the expression ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 can be resolved into two linear rational factors if Δ = abc + 2fgh − af^2 − bg^2 − ch^2 = 0

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{expression}\:{ax}^{\mathrm{2}} \:+\:\mathrm{2}{hxy} \\ $$$$+\:{by}^{\mathrm{2}} \:+\:\mathrm{2}{gx}\:+\:\mathrm{2}{fy}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{resolved}\:\mathrm{into}\:\mathrm{two}\:\mathrm{linear}\:\mathrm{rational}\:\mathrm{factors} \\ $$$$\mathrm{if}\:\Delta\:=\:{abc}\:+\:\mathrm{2}{fgh}\:−\:{af}^{\mathrm{2}} \:−\:{bg}^{\mathrm{2}} \:−\:{ch}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$

Question Number 20293 Answers: 1 Comments: 0

∫(√(((a+x)/x)dx))

$$\int\sqrt{\frac{{a}+{x}}{{x}}{dx}} \\ $$

Question Number 20292 Answers: 1 Comments: 0

∫(dx/((x+1)^(1/2) +(√(x−1))))

$$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} +\sqrt{{x}−\mathrm{1}}} \\ $$

Question Number 20291 Answers: 1 Comments: 0

(√(((1−x)/(1+x)) dx))

$$\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\:{dx}} \\ $$

Question Number 20296 Answers: 2 Comments: 0

If (m_r , (1/m_r )) ; r = 1, 2, 3, 4 be four pairs of values of x and y satisfy the equation x^2 + y^2 + 2gx + 2fy + c = 0, then prove that m_1 .m_2 .m_3 .m_4 = 1.

$$\mathrm{If}\:\left({m}_{{r}} \:,\:\frac{\mathrm{1}}{{m}_{{r}} }\right)\:;\:{r}\:=\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{be}\:\mathrm{four}\:\mathrm{pairs} \\ $$$$\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{gx}\:+\:\mathrm{2}{fy}\:+\:{c}\:=\:\mathrm{0},\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{m}_{\mathrm{1}} .{m}_{\mathrm{2}} .{m}_{\mathrm{3}} .{m}_{\mathrm{4}} \:=\:\mathrm{1}. \\ $$

Question Number 20449 Answers: 0 Comments: 0

∫(dx/(sin^(1/2) xcos^(7/2) x))

$$\int\frac{{dx}}{\mathrm{sin}\:^{\frac{\mathrm{1}}{\mathrm{2}}} {x}\mathrm{cos}\:^{\frac{\mathrm{7}}{\mathrm{2}}} {x}} \\ $$

Question Number 20259 Answers: 1 Comments: 0

Find the number of real roots of the equation f(x) = x^3 + 2x^2 + 2x + 1 = 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 20257 Answers: 1 Comments: 0

∫(dx/((1−x)(√(1+x))))

$$\int\frac{{dx}}{\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}+{x}}} \\ $$

Question Number 20256 Answers: 1 Comments: 0

∫(dx/((x−4)(√(x+3))))

$$\int\frac{{dx}}{\left({x}−\mathrm{4}\right)\sqrt{{x}+\mathrm{3}}} \\ $$

Question Number 20255 Answers: 1 Comments: 0

∫((x^3 dx)/(√(x−1)))

$$\int\frac{{x}^{\mathrm{3}} {dx}}{\sqrt{{x}−\mathrm{1}}} \\ $$

Question Number 20254 Answers: 1 Comments: 0

∫(dx/((x−1)(√(x^2 +1))))

$$\int\frac{{dx}}{\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} \\ $$

Question Number 20281 Answers: 0 Comments: 0

Compute the volume bounded by the surfaces: y=x^2 , x=y^2 , z=0, z=12+y−x^2 . [ Ans. ((549)/(144))]

$${Compute}\:{the}\:{volume}\:{bounded}\:{by} \\ $$$${the}\:{surfaces}:\:{y}={x}^{\mathrm{2}} ,\:{x}={y}^{\mathrm{2}} ,\:{z}=\mathrm{0}, \\ $$$${z}=\mathrm{12}+{y}−{x}^{\mathrm{2}} .\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\:{Ans}.\:\:\:\:\frac{\mathrm{549}}{\mathrm{144}}\right] \\ $$

Question Number 20245 Answers: 2 Comments: 0

y=2^(1/(log_x 8)) then x=?

$$\mathrm{y}=\mathrm{2}^{\frac{\mathrm{1}}{{log}_{{x}} \mathrm{8}}} \\ $$$${then}\:{x}=? \\ $$

Question Number 20244 Answers: 1 Comments: 0

∫(dx/((2−x)(√x)))

$$\int\frac{{dx}}{\left(\mathrm{2}−{x}\right)\sqrt{{x}}} \\ $$

Question Number 20243 Answers: 1 Comments: 0

∫(dx/(x+(√x)))

$$\int\frac{{dx}}{{x}+\sqrt{{x}}} \\ $$

Question Number 20242 Answers: 1 Comments: 0

∫((5x^2 +11x+26)/(x^2 +2x+5))dx integration by partial fraction

$$\int\frac{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{26}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}{dx} \\ $$$${integration}\:{by}\:{partial}\:{fraction} \\ $$

Question Number 20241 Answers: 1 Comments: 0

partial fraction ∫((2x^2 +5x−9)/(√(x^2 −x+1)))dx

$${partial}\:{fraction} \\ $$$$\int\frac{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{9}}{\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}}{dx} \\ $$

Question Number 20279 Answers: 0 Comments: 0

Determine a relation between the coefficients a, b, c, d such that the equation: ax^3 +bx^2 +cx+d=0 has three real roots (with a pair of double roots).

$${Determine}\:{a}\:{relation}\:{between}\:\:{the} \\ $$$${coefficients}\:\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{d}}\:{such}\:{that}\:{the} \\ $$$${equation}:\:\:{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${has}\:{three}\:{real}\:{roots}\:\left({with}\:{a}\:{pair}\right. \\ $$$$\left.{of}\:{double}\:{roots}\right). \\ $$

Question Number 20239 Answers: 1 Comments: 0

∫(((2x+3)dx)/(√(x^2 +4x−7)))

$$\int\frac{\left(\mathrm{2}{x}+\mathrm{3}\right){dx}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{7}}} \\ $$

Question Number 20238 Answers: 1 Comments: 1

∫(dx/(x^2 −x+1))

$$\int\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$

Question Number 20237 Answers: 0 Comments: 1

∫(e^(tan^(−1) x) /(1+x^2 ))dx

$$\int\frac{{e}^{\mathrm{tan}^{−\mathrm{1}} {x}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 20235 Answers: 0 Comments: 1

if t_((m+1)) =2t_((n+1)) so proof t_((3m+1)) =2t_((m+n+1) ) help please.........

$$ \\ $$$${if}\:\:\:\:\:\:\:\:{t}_{\left({m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({n}+\mathrm{1}\right)} \\ $$$${so}\:{proof} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{t}_{\left(\mathrm{3}{m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({m}+{n}+\mathrm{1}\right)\:\:\:\:\:\:} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{help}\:{please}......... \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 20230 Answers: 1 Comments: 5

Question Number 20217 Answers: 0 Comments: 1

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