Recently Active Algebra Questions

\hspace{-16}$Find value of $\mathbf{x}$ in $\mathbf{\sqrt{2x^2-4x+4}+\sqrt{2x^2-12x+26}=\sqrt{26}}$ ...

Q1} How many ordered triples (a,b,c) of positive integers are there such that none of a,b,c exceeds 2010 and each of a,b,c divides a+b+c ? Q2} Let n be a positive integer. Prove that there are no positive integers x and y suc ...

Find all integers 'n' such that (7n-12)/2^n + (2n-14)/3^n + (24n)/6^n = 1 ...

I always was and am confused with POSITIVE and NEGATIVE signs for the square roots!So,please answer these seemily STUPID questions [1] so that i remain no longer confused! √4=? 41/2=? ...

consider 5-digit numbers formed using the digits 0,1,2,3,4,5 without repetition of digits. Q) the number of numbers divisible by 4 is ? Q) the number of numbers divisible by 12 is? Q) the number of numbers divisible by 15 is ...

\hspace{-16}$Find value of $\mathbf{x}$ in $\mathbf{2^x+2^{\left[x\right]}+2^{\left\{x\right\}}=3}$\\\\ Where $\mathbf{\left[.\right]=}$ Greatest Integer Function and \\\\ $\mathbf{\left\{.\right\}=}$ fractional part function ...

Let a, b, c be positive reals such that a + b + c = 1. Prove that ( a/1 + 1/b )( b/1 + 1/c )( c/1 + 1/a ) ≥ (10/3)3 ...

Determine all distinct triangles having one side of length 6,with the other two sides being integers ,and perimeter numerically equal to the area. ...

prove that for a , b , c in [0,infinty) (a - 1/b)(b - 1/c)(c- 1/a) ≥ (a - 1/a)(b - 1/b)( c-1/c). here (a - 1/b) means a/1 - 1/b ...

Solve the equation (x^4 + 5x^3 + 8x^2 + 7x + 5)^4 + (x^4 + 5x^3 + 8x^2 + 7x + 3)^4 = 16 in the set of real numbers. ...

Find all (x, y) where x and y are positive integers such that x^{2007} = y^{2007} − y^{1338} − y^{669} + 2. i found one pair to be (1,1) also 2007 = 3(669) and 1338 = 2(669). don't know but it might help. ...

\hspace{-16}$If $\mathbf{p,q,r>0\;}$,Then find $\mathbf{p,q,r}$ in \\\\ $\mathbf{\ln\left(pqr\right)=-2}$\\\\ $\mathbf{ln(p).\ln(q).\ln(r)=2}$\\\\ $\mathbf{\ln(p).\ln(q)+\ln(q).\ln(r)+\ln(r).\ln(p)=-1}$ ...

can anyone tell me how to find the number of prime nos between two given integers eg:: between 1 to 10 there are 4 primes .......please tell me if there is any general method for this. ...

A person has got 15 aquantances of which 10 are relatives. In how many ways he may invite 9 guests so that 7 would be relatives? [I am a beginner so please explain the result] ...

Let H be a finite set of positive integers none of which has a prime factor greater than 3.Show that the sum of the reciprocals of the elements of H is smaller than 3. ...

how many ways can the word VENUS be arranged so that the vowels do not change thein orders?? ...

\hspace{-16}$If $\alpha,\;\beta,\;\gamma$ be The roots of the equation$ \\\\ \left\{\begin{matrix} \alpha^3+a.\alpha+b=0\\\\ \beta^3+a.\beta+b=0\\\\ \gamma^3+a.\gamma+b=0 \end{matrix}\right.\\\\\\ $Then $a\lpha+\beta+\gamma=$ ...

If x , y , z are three real numbers not equal to 1 such that xyz=1 show that : x2/(x-1)2 + y2/(y-1)2 + z2/(z-1)2 ≥1 ...

$\hspace{-16}\textbf{(1)\;Solve the equation z^4=\bar{z}}:$\\\\ $\textbf{(2)\;If Z\in\mathbb{C}\textbf{\;and $\mid z\mid<\frac{1}{2}.$ Then Show that }}$\\\\ \mathbf{\mid (1+i).z^3+iz\mid<\frac{3}{4} } ...

Let Tn = 1 + 2 + 3 + · · · + n and Pn = T2/T2-1 . T3/T3-1 . T4/T4-1 ....... Tn/Tn-1 Find Pn???? ...

\hspace{-16}\textbf{Solve the equation for real x}:\\\\ \mathbf{4^x.9^{\frac{1}{x}}+9^x.4^{\frac{1}{x}}=210} ...

\hspace{-16}$Find all Polynomials $p(x)$ such that $(x-1).p(x)+1=x.p(x+1)$ ...

The least positive integer n for which ( 1+i/1-i )n= 2/π sin-1( 1+x2/2x ) x≥0 ...

A book contains pages numbered from 1 to 50. 4 leaves (i. e., 8 pages) were torn off the book. What is the probability that the sum of the page numbers is 68? ...

find the sum to infinity....1/2.4+1.3/2.4.6+1.3.5/2.4.6.8 ....... ...

if a + 2b + c = 4 then find the max(ab + bc + ac) ...

sorry for multiple posting ...

Please post a detailed explanatory solution to the following. *Image* Thanks ...

the argument of (1- i 3 ) is (1+ i 3 ) A) 60° B) 120° C) 210° D) 240° i got the answer as 240° but the book ans says it is 60°.... 'am baffled!! ...

Express (1+x2) (1+y2) (1+z2) as sum of two squares. ...