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AlgebraQuestion and Answers: Page 277

Question Number 85554 Answers: 0 Comments: 1

2x^2 +5x+7=0

$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$

Question Number 85532 Answers: 1 Comments: 0

Find the term independent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Question Number 85490 Answers: 0 Comments: 3

Given that the expression 2x^3 +px^2 −8x+9 is exactly divisable by x^2 −6x+5, find the value of p and q. Hence factorise the expression fully

$${Given}\:{that}\:{the}\:{expression}\:\mathrm{2}{x}^{\mathrm{3}} +{px}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{9}\:{is}\:{exactly}\:{divisable}\:{by}\:{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5},\:{find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{q}}.\:{Hence}\:{factorise}\:{the}\:{expression}\:{fully} \\ $$

Question Number 85418 Answers: 0 Comments: 1

Find the term indepent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{indepent}\:{of}\:{x}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Question Number 85413 Answers: 0 Comments: 0

Question Number 85412 Answers: 0 Comments: 1

Question Number 85365 Answers: 3 Comments: 0

Question Number 85358 Answers: 1 Comments: 0

((x ))^(1/(3 )) + (√x) = 12

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}\:}\:+\:\sqrt{\mathrm{x}}\:=\:\mathrm{12} \\ $$

Question Number 85322 Answers: 0 Comments: 10

please help me to solve this in N A_n ^2 −3C_n ^( n−2) +n=−20

$${please}\:{help}\:{me}\:{to}\:{solve}\:{this}\:{in}\:\mathbb{N} \\ $$$${A}_{{n}} ^{\mathrm{2}} −\mathrm{3}{C}_{{n}} ^{\:{n}−\mathrm{2}} +{n}=−\mathrm{20} \\ $$

Question Number 85318 Answers: 0 Comments: 1

Question Number 85249 Answers: 0 Comments: 0

Question Number 85240 Answers: 0 Comments: 0

Question Number 85228 Answers: 0 Comments: 2

Question Number 85224 Answers: 0 Comments: 7

solve in N (n−4)!=42(n−2)!

$${solve}\:{in}\:\mathbb{N} \\ $$$$\left({n}−\mathrm{4}\right)!=\mathrm{42}\left({n}−\mathrm{2}\right)! \\ $$

Question Number 85183 Answers: 0 Comments: 1

Hi veterans Serlea (1) Find the last three digits of: 3005^(11) +3005^(12) +3005^(13) +...+3005^(3002)

$$\mathrm{Hi}\:\mathrm{veterans} \\ $$$$\mathrm{Serlea}\:\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{three}\:\mathrm{digits}\:\mathrm{of}: \\ $$$$\mathrm{3005}^{\mathrm{11}} +\mathrm{3005}^{\mathrm{12}} +\mathrm{3005}^{\mathrm{13}} +...+\mathrm{3005}^{\mathrm{3002}} \\ $$$$ \\ $$$$ \\ $$

Question Number 85176 Answers: 2 Comments: 0

what is range function y = (√(x−1)) + (√(5−x))

$$\mathrm{what}\:\mathrm{is}\:\mathrm{range}\: \\ $$$$\mathrm{function}\:\mathrm{y}\:=\:\sqrt{\mathrm{x}−\mathrm{1}}\:+\:\sqrt{\mathrm{5}−\mathrm{x}} \\ $$

Question Number 85104 Answers: 1 Comments: 2

Given { ((x^2 −2xy−3x = −1)),((4y^2 −2xy+6y = −1)) :} find 2y − x

$$\mathrm{Given}\: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{2xy}−\mathrm{3x}\:=\:−\mathrm{1}}\\{\mathrm{4y}^{\mathrm{2}} −\mathrm{2xy}+\mathrm{6y}\:=\:−\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{2y}\:−\:\mathrm{x} \\ $$

Question Number 85103 Answers: 0 Comments: 0

Question Number 84941 Answers: 2 Comments: 1

Question Number 84915 Answers: 1 Comments: 0

if x>0,y>0,z>0 show that ((x+y)/z)+((z+y)/( x))+((z+x)/y)≥6

$${if}\: \\ $$$${x}>\mathrm{0},{y}>\mathrm{0},{z}>\mathrm{0} \\ $$$${show}\:{that} \\ $$$$\frac{{x}+{y}}{{z}}+\frac{{z}+{y}}{\:{x}}+\frac{{z}+{x}}{{y}}\geqslant\mathrm{6}\:\: \\ $$

Question Number 84913 Answers: 2 Comments: 2

sin(π/(14)) sin((3π)/(14)) sin((5π)/(15))=?

$$ \\ $$$${sin}\frac{\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{3}\pi}{\mathrm{14}}\:{sin}\frac{\mathrm{5}\pi}{\mathrm{15}}=? \\ $$

Question Number 84891 Answers: 0 Comments: 0

Question Number 84871 Answers: 1 Comments: 1

If you know (((b^2 +c^2 −a^2 )/(2bc)))^2 +(((c^2 +a^2 −b^2 )/(2ca)))^2 +(((a^2 +b^2 −c^2 )/(2ab)))^2 =3, then what′s the value of ((b^2 +c^2 −a^2 )/(2bc))+((c^2 +a^2 −b^2 )/(2ac))+((a^2 +b^2 −c^2 )/(2ab))?

$$\mathrm{If}\:\mathrm{you}\:\mathrm{know} \\ $$$$\left(\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}\right)^{\mathrm{2}} +\left(\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ca}}\right)^{\mathrm{2}} +\left(\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}\right)^{\mathrm{2}} =\mathrm{3}, \\ $$$$\mathrm{then}\:\mathrm{what}'\mathrm{s}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{2}{bc}}+\frac{{c}^{\mathrm{2}} +{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{2}{ac}}+\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{2}{ab}}? \\ $$

Question Number 84835 Answers: 0 Comments: 1

Question Number 84820 Answers: 1 Comments: 0

Question Number 84792 Answers: 0 Comments: 0

a,b,c≥0 a+b+c=3 show that (a)^(1/3) +(b)^(1/3) +(c)^(1/3) ≥ab+bc+ca

$${a},{b},{c}\geqslant\mathrm{0} \\ $$$${a}+{b}+{c}=\mathrm{3} \\ $$$${show}\:{that} \\ $$$$\sqrt[{\mathrm{3}}]{{a}}\:+\sqrt[{\mathrm{3}}]{{b}}\:+\sqrt[{\mathrm{3}}]{{c}}\geqslant{ab}+{bc}+{ca} \\ $$

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