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AlgebraQuestion and Answers: Page 32

Question Number 210689 Answers: 1 Comments: 0

Question Number 210685 Answers: 3 Comments: 0

find ∫(1/x)dx

$${find} \\ $$$$\int\frac{\mathrm{1}}{{x}}{dx} \\ $$

Question Number 210666 Answers: 1 Comments: 0

prove that p(n) is integer ∀ n∈Z p(n) = ((3n^7 +7n^3 +11n)/(21))

$$\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{p}\left(\mathrm{n}\right)\:\mathrm{is}\:\mathrm{integer}\:\forall\:\mathrm{n}\in\mathbb{Z} \\ $$$$\:\:\:\mathrm{p}\left(\mathrm{n}\right)\:=\:\frac{\mathrm{3n}^{\mathrm{7}} +\mathrm{7n}^{\mathrm{3}} +\mathrm{11n}}{\mathrm{21}} \\ $$

Question Number 210661 Answers: 0 Comments: 0

Question Number 210660 Answers: 0 Comments: 0

Question Number 210659 Answers: 0 Comments: 0

Question Number 210652 Answers: 0 Comments: 0

Question Number 210643 Answers: 3 Comments: 0

Question Number 210639 Answers: 3 Comments: 0

given that the roots of the equation 3x^2 −(4+2k)x+2k=0 are α and β find the value of k for which β=3α

$${given}\:{that}\:{the}\:{roots} \\ $$$$\:{of}\:{the}\:{equation} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} −\left(\mathrm{4}+\mathrm{2}{k}\right){x}+\mathrm{2}{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta \\ $$$${find}\:{the}\:{value}\:{of}\:{k} \\ $$$${for}\:{which}\:\beta=\mathrm{3}\alpha \\ $$

Question Number 210630 Answers: 1 Comments: 0

Question Number 210629 Answers: 2 Comments: 0

Question Number 210679 Answers: 2 Comments: 0

Question Number 210608 Answers: 2 Comments: 1

Question Number 210606 Answers: 2 Comments: 0

Question Number 210591 Answers: 3 Comments: 0

If a + b = 1 a^2 + b^2 = 2 then, a^(11) + b^(11) = ??

$$\mathrm{If} \\ $$$$\:\:\:\:\mathrm{a}\:\:+\:\:\mathrm{b}\:\:=\:\:\mathrm{1} \\ $$$$\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{b}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\mathrm{then},\:\:\:\:\:\mathrm{a}^{\mathrm{11}} \:\:+\:\:\mathrm{b}^{\mathrm{11}} \:\:=\:\:?? \\ $$

Question Number 210590 Answers: 0 Comments: 0

Question Number 210587 Answers: 0 Comments: 3

f(x)= (√( 13 −12(√x) )) + (√(25 −24(√(1−x)) )) find : Min ( f )=?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mathrm{13}\:−\mathrm{12}\sqrt{{x}}\:\:}\:+\:\sqrt{\mathrm{25}\:−\mathrm{24}\sqrt{\mathrm{1}−{x}}\:} \\ $$$$ \\ $$$$\:\:\:\:\:\:{find}\::\:\:\:\:\mathrm{M}{in}\:\left(\:{f}\:\right)=? \\ $$$$ \\ $$$$ \\ $$

Question Number 210581 Answers: 1 Comments: 0

{ ((x^2 +3x−(√(x^2 +3x−1 = 7)))),((2(√2) sin y = x)) :} x=? and y=?

$$\:\:\begin{cases}{{x}^{\mathrm{2}} +\mathrm{3}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{1}\:=\:\mathrm{7}}}\\{\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{sin}\:{y}\:=\:{x}}\end{cases} \\ $$$$\:\:\:{x}=?\:\:\:\:{and}\:\:\:\:{y}=? \\ $$

Question Number 210579 Answers: 0 Comments: 4

Please... Can anyone help me.. Find the value(s) of x, if (x−2)^((x^2 −2x+4)) =3

$${Please}...\:{Can}\:{anyone}\:{help}\:{me}.. \\ $$$$ \\ $$$$\:{Find}\:{the}\:{value}\left({s}\right)\:{of}\:{x},\:{if} \\ $$$$\:\:\:\left({x}−\mathrm{2}\right)^{\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}\right)} =\mathrm{3} \\ $$$$ \\ $$

Question Number 210574 Answers: 3 Comments: 0

if the roots of the equation x^2 +(k+1)x+k=0 are α and β, find the value of the real constant k for which α=2β

$${if}\:{the}\:{roots}\:{of}\:{the}\:{equation}\: \\ $$$${x}^{\mathrm{2}} +\left({k}+\mathrm{1}\right){x}+{k}=\mathrm{0} \\ $$$${are}\:\alpha\:{and}\:\beta, \\ $$$$\:{find}\:{the}\:{value}\:{of}\:{the} \\ $$$$\:{real}\:{constant}\:{k}\:{for} \\ $$$${which}\:\alpha=\mathrm{2}\beta \\ $$

Question Number 210573 Answers: 1 Comments: 0

Question Number 210572 Answers: 1 Comments: 0

Question Number 210571 Answers: 1 Comments: 0

If x,y,z∈R^+ and x^2 +y^2 +z^2 =3 Prove that (1/(4−x)) + (1/(4−y)) + (1/(4−z)) ≤ 1

$$\mathrm{If}\:\:\mathrm{x},\mathrm{y},\mathrm{z}\in\mathrm{R}^{+} \:\:\mathrm{and}\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}−\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{z}}\:\:\leqslant\:\:\mathrm{1} \\ $$

Question Number 210565 Answers: 1 Comments: 0

Question Number 210559 Answers: 1 Comments: 0

deg [p(x^2 )∙q(x)]=20 deg[((p(x)^3 )/(q(x)^2 ))]=2 then deg q(x)=?

$${deg}\:\left[{p}\left({x}^{\mathrm{2}} \right)\centerdot{q}\left({x}\right)\right]=\mathrm{20} \\ $$$${deg}\left[\frac{{p}\left({x}\right)^{\mathrm{3}} }{{q}\left({x}\right)^{\mathrm{2}} }\right]=\mathrm{2} \\ $$$${then}\:{deg}\:\:{q}\left({x}\right)=? \\ $$

Question Number 210533 Answers: 1 Comments: 1

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