Recently Active Algebra Questions

if roots of the equation x2-10cx-11d=0 are a,b and those of x2-10ax-11b=0 are c,d,then find the value of (a+b+c+d)? ...

The number of distinct terms in the expansion of ( 1/xy + 1/zy + 1/xz +x+y+z)2 and ( 1/z + 1/y + 1/x +x+y+z)2 are? ...

Please see this question here. http://www.artofproblemsolving.com/Forum/viewtopic.php?f=296&t=454883&p=2556669#p2556669 ...

\hspace{-16}$If $\mathbf{a,b\in\mathbb{Z^{+}}}.$ Then prove that $\mathbf{\frac{a}{b}<\sqrt{2}<\frac{a+2b}{a+b}}$ ...

If p + q = 1, then show that *Image* ...

\hspace{-16}$Determine all Positive Integer that satisfy $\mathbf{\frac{1}{x}+\frac{2}{y}+\frac{3}{z}=1!}$\\\\ ...

\hspace{-16}$The no. of solution of the equation $\mathbf{ae^x=1+x+\frac{x^2}{2}}$\\\\ Where $a>0$ ...

\hspace{-16}$If $\mathbf{n}$ be a Positive Integer Then Prove that\\\\\\ $\mathbf{\frac{1}{\binom{2009}{1}}+\frac{1}{\binom{2009}{2}}+\frac{1}{\binom{2009}{3}}+..............+\frac{1}{\binom{2009}{n+1}}<\frac{1}{2007}}$ th ...

\hspace{-16}$Find all positive Integer $\mathbf{x\;,y\;,z}$ such that \\\\ $\mathbf{x!=4y!+10z!}$ ...

Let x,y be two nonzero real numbers with a,b real show that : a2| x/y |+b2| y/x |≥2ab ...

If x,y>0 show that : 1/x+y < 1/x + 1/y ...

1) Find the total no.of +ve integral solutions of the inequality 3x+y+z<= 30.. Can a student not knowing multinomial theorem solve this Problem?? ...

How many times does the Number 5 appear in front of you when you start writing numbers from 1 to 105 in a row..???? ...

if you have infinite no of Rs.10,20 nd 50 notes....in how many ways can u give a person Rs.1000? i tried dis... getting to find the no of integral solutions to a+2b+5c =100 how to proceed after this? ...

Q.1 Four dice are rolled once. Find the number of ways in which one die shows at least 3. Q.2 A die is rolled 10 times. Find the number of ways so that the outcomes always contain 1,2,3. ...

Show that there is no in finite arithmetic progression consisting of distinct integers all of which are squares. ...

4 letters, 2 a's and 2 b's, are to be used for filling 16 cells of a 4* 4 matrix. It is required that each cell contains at most 1 letter, and no row or column can contain two same letters. The number of ways in which such a ...

If I hav a misconception please clear let Z be a complex no. = 2+3i... in Argands plane the coordinate of the complex no. is (2,3i) now we know that modulus of z = r that is the distance of the coordinate from origin.... now ...

find the largest and the smallest 7 digit number formed by the digits from 1 to 9 such that there is no repetition of digits and the number is divisible by all the digits. ...

For the three events A, B and C. P (exactly one of events A or B occurs) = P (exactly one of events B or C occurs) = P (exactly one of events C or A occurs) = p and P (all events occur simultaneously) = p2, where 0 < p < ...

\hspace{-16}$Find the smallest positive Integer $\mathbf{n}$ such that \\\\ $\mathbf{\sqrt{n}-\sqrt{n-1}<0.01}$ ...

Calculate the sum: √1+1/1^2 +1/2^2 + √1+1/2^2 +1/3^2 + ...........+√1+1/2007^2 + 1/2008^2 ...

\hspace{-16}$Show that regardless of what Integer values of $\mathbf{x\;,y}$ Substituted\\\\ in $\mathbf{x^5-x^4y-13x^3y^2+13x^2y^3+36xy^4-36x^5}$ is never equal to $\mathbf{77}$ ...

*Image* Circle has radius 2 units. help me finding the area! ...

1) Solve for x: [x2]= x +2{x} [ ] denotes the G.I.F.{ } is the fractional part. 2) Find the total number of integral solutions of x2-2y2 =2000. ...

\hspace{-16}$Which of the following no. is Greater\\\\ $\mathbf{A=\frac{2.0000004}{(1.0000004)^2+2.0000004}}$ OR $\mathbf{B=\frac{2.0000002}{(1.0000002)^2+2.0000002}}$ ...

find the number of points (x,y) with positive integral coordinates satisfying the x^2 + y^2 + 2xy - 2005x - 2005y - 2006 = 0. ...

(258+1)/5 is a prime number or a composite one???? Please give the proof along with it. ...

\hspace{-16}$How Many Positive Integer Solution $\mathbf{(a,b,c)}$ are\\\\ there to the equation $\mathbf{2004^a+2005^b=2006^c}$ ...

If A and G be A.M & G.m respectively between two positive numbers,prove that the numbers A± (A+G)(A-G) ...