Recently Active Algebra Questions

Find the area enclosed by x3+y3-3xy=0 ...

A player tosses a coin and is to score one point for every head and one point for every tal.He is to play on until his score reaches or passes n.If Pn is hte chance of getting exactly n,show that Pn=(Pn-1+Pn-2)/2 . Also find ...

Find the sum to n terms: 1\1*3 + 2\1*3*5 + 3\1*3*5*7......to n terms. ...

3 fair special dice whose face numbers are -3,-2,-1,0,1,2, are rolled .Find probablty that sum of digits on faces is 3 ...

[we're 2005 while writing] According to a legend there is a monster that awakes every now and then to swallow everyone who is solving this problem, and then falls back asleep for as many years as the sum of the digits of that ...

The number of natural numbers less than 2.104 which can be formed with digits 1,2,3 only are ? ...

If a,b are the roots of x2+px+1=0 and c,d are the roots of x2+qx+1=0 then show that q2-p2=(a-c)(b-c)(a+d)(b+d) ...

Suppose the complex number z satisfies the equation 11z^{10}+10iz^9+10iz-11=0 Prove that |z|=1 . ...

Q1 Let n and m be any two 3 digit numbers .Find total number of pairs of n and m so that n and m can be added without carrying Q2Let n and m be any two 3 digit numbers .Find total number of pairs of n and m so that n can be s ...

Prove that there are no perfect squares in the array below: 11 111 1111 ... 22 222 2222 ... 33 333 3333 ... 44 444 4444 ... .. .. .. 99 999 9999 ... ...

Let a and b be two primes having at least two digits, such that a > b. Show that 240 divides a4-b4. ...

1. If a,b,c be +ve real nos,prove that: a/(b+c) +b/(c+a) + c/(a+b) >= 3/2 ...

1) The eqn (cos p -1) x2 + (cosp)x + sinp =0, in the variable x ,has real roots. Then p can have any value in the interval (a) (0 , 2 pie) (b) (- pie, 0 ) (c) (- pie/2 , pie/2 ) (d) ( 0 ,pie) ...

Four couples play chess together. For the match, they're paired as follows: ("man Clara" indicates the husband of Clara, etc.) Bea ≡ Eddy An≡ man Clara Freddy ≡woman Guy Debby ≡ man An Guy ≡ woman Eddy Who is Hubert ...

Given a cube in which you can put two massive spheres of radius 1. What's the smallest possible value of the side - length of the cube? Prove that your answer is the best possible. ...

Q1 If a≠b,then equation zz+az+bz+c=0 represents ? Q2 If a=b,c εR and lbl2>c ,then equation zz+az+bz+c=0 represents ? Q3 If a=b,c εR and lbl2<c ,then equation zz+az+bz+c=0 represents ? ...

hey guyys a nice sum.... plz try it outt if there r n points on a circle....no. of triangles that can be formed by joining them.....note:no three lines intersect at a point.....[the answer iss not nC3 u have to consider the s ...

1) Show that the soln set of eqns (x+1) 2 + [x-1] 2 = (x-1)2 + [x+1] 2 , where [x] and (x) are the gratest integer and nearest integer to x , is x belonging to I. 2) If P(x) = ax 2+bx+c and Q(x) = -ax 2+dx+c, where ac≠0, th ...

*Image* I suddenly encountered this inequality (While attempting another one [78] ), which seemingly seems true....(I mean I checked with a few values....) but i've not been able to prove it, as it is I do not even know wheth ...

Please solve these problems 1. (x-a)(x-a)(x-a) + (x-b)(x-b)(x-b) + (x-c)(x-c)(x-c) = 0 has A)All the roots real B)one real and two imaginary roots C)three real roots namely x=a,x=b,x=c D)None 2. a+b+c = 0, then the quadratic ...

Prove that the sum of the infinite series 1+1-1+1-1+... is either 1 or 0. <edited:> the sum can be 1/2 too.. in fact, the sum is formally defined to be 1/2. So...go ahead and prove it! ...

The number of cubic polynomials p(x) with integral co-efficients such that for three distinct integers a, b and c such that p(a)=b, p(b)=c and p(c)=a is (a) 0 (b) 1 (c) dependent on a, b, c (d) infinite ...

The following is a system of quadratic equation with a,b,c being real and a≠0..... ax12+bx1+c=x2 ax22+bx2+c=x3 ax32+bx3+c=x4 ax42+bx4+c=x5 . . . . . . . . axn-12+bxn-1+c=xn axn2+bxn+c=x1 Answer the following questions.... Q ...

1) SHow that the roots of the eqn x4+4x3-8x2+k=0 are real for k belonging to [0,3]. 2) Show that the eqn log(x2+2ax) = log(8x-6a-3) have only one solution for a=1 or a belonging to [-1/2 , -3/22]. ...

This was posted in another iitian forum (by one of our members :D). Its a nice problem so I flicked it. Let f(x) = ax2+bx+c be such that the equation f(x) = x has non-real roots. Prove that this implies that the equation f(f( ...

A square has tens digit 7.Find its units digit I want to learn the basic concept of this question more than just the answer :-) ...

If a<b<c<d , then the equation (x-a)(x-c) + 2(x-b)(x-d) = 0 has a)Imaginary roots b)equal roots c)distinst real roots d) none 2. If α is a root of a2x2 + bx + c=0 , β is a root of a2x2 -bx - c=0 and α<β , then ...

Let k and n be positive integers and put Sk=Σnk (n varies from 1 to n. show that m+1C1S1+m+1C2S2...............+m+1CmSm=(n+1)m+1-(n+1) ...

If a+b+c=0 and a,b,c are real, then prove that the eqn (b-x)2 - 4 (a-x)(c-x) = 0 has real roots and the roots will not be equal unless a=b=c. ...

Ques1) Prove that the sum of 1 st n odd natural numbers is n2 and hence or otherwise prove that the sum of next 'n' odd natural numbers is divisible by 3. Ques2) Show that the sum of 2/3 + 8/9 + 26/27 + 80/81 + .............u ...