Recently Active Algebra Questions

The equation A2/(x-a) + B2/(x-b) + C2/(x-c) + ..... + H2/(x-h) = k has 1) No real root 2) At most one real root 3) No complex root 4) At most two complex roots ...

If one root of ax^2+bx-2c=0 (a,b,c are real) is imaginary and 8a+2b>c , then a) a>0 and c<0 b)a>0 and c>0 c)a<0,c>0 d)a<0,c<0 ...

1/(1*4) +1/(4*7)+1/(7*10)+......................∞=? ...

1) x\sqrt{y}+y\sqrt{x}=20 x\sqrt{x}+y\sqrt{y}=65 2) 3x+4x+5x =6x 3) Find all the roots of the equation : 4x4 – 24x3 + 57x2 + 18x – 45 = 0 if one root is 3 + i 6 . ...

How to draw the graph of y≥x2-1? If x=1 then y≥0.So,where to find this point as y can be anywhere? ...

Problem 1: If a1,a2,.........an-1,an are in AP prove: 1/(a1an) + 1/(a2an-1)+1/(a3an-2)+..............+1/(ana1)=[2/(a1+an)][1/a1 + 1/a2+ 1/a3 +.........+ 1/an] ...

Find 3-digit numbers that are divisible by 5 as well as 9 and whose consecutive digits are in A.P ...

Let z and w be two complex numbers such that \bar{z} +i\bar{w} =0 and arg zw=∩ , then arg z is equal to ? ...

$\textbf{ If $\mathbf{\alpha,\beta,\gamma}$ be the Roots of the equation $\mathbf{x^3+2x^2-3x-1=0}$.\\\\ Then find the value of $\mathbf{\frac{1}{\alpha^5}+\frac{1}{\beta^5}+\frac{1}{\gamma^5}=}$} ...

$\textbf{Solve Inequality:}\\\\ $\mathbf{3^x+4^x+6^x+8^x+15^x=5^x+9^x+10^x+12^x\forall x\in\mathbb{R} } ...

$\textbf{Calculate value of $\mathbf{x}$ in $\mathbf{2\cdot \left\{x\right\}=3[x]-[x^2]}$ }\\\\ \textbf{Where $\mathbf{\left\{.\right\}$= Fractional Part of $\mathbf{x}$}}\\\\ \textbf{and $\mathbf{[.]=}$ Integer Part}$ ...

\left|x-2 \right|^{log_{2}x^{3}-3log_{x}4} = (x-2)^{3} ...

$Solve The Equation $\mathbf{2012^x-2011^x=1+3\left(2011^{\frac{x}{3}}+2011^{\frac{2x}{3}}\right)}$\\\\ \mathbf{Ans:=}::$\mathbf{x=3}$ ...

\textbf{Solve The equation}:\\\\ \mathbf{\sqrt{4^x-6^x+9^x}+\sqrt{9^x-3^x+1}+\sqrt{4^x-2^x+1}=2^x+3^x+1} ...

I request forum experts and Mods to provide some links to websites where i can find material on HOW TO NORMALISE A SEQUENCE! ...

5x/2-2x=1 ...

1. Find the sum of the products of every pair of the first n natural numbers 2. Sum the series : 1 + 4 + 10 + 22 + 46 + ...... to n terms. 3. Find the sum of first n terms of the series : 1(1)! + 2(2) ! + 3(3)! + 4(4)! + .... ...

(2+\sqrt{3})^{x^{2}-2x+1} +(2-\sqrt{3})^{x^{2}-2x-1}=\frac{2}{2-\sqrt{3}} ...

$\textbf{If $\mathbf{a^2+b^2+c^2=3}$.Then find Max. value of $\mathbf{a+b+c-3abc}$} ...

xy+x+y=23 xz+x+z=41 yz+y+z=27 ...

If xyz=1, x+1/z=5; y+1/x=29, then z+1/y=? ...

x^{2}+y(x+1)=17 y^{2}+x(y+1)=13 ...

$\textbf{Calculate real values of $\mathbf{x}$ in\\\\ $\mathbf{27^x+125^x+343^x+1331^x=105^x+165^x+231^x+385^x}$} ...

1. a4 + b4 + c4 > 3abc (a + b + c) 2. if x = 2 + 21/3 + 22/3, then find x3 - 6x3 + 6x Please please please......... solve these.... ...

$\textbf{Find Minimum value of $\mathbf{f(x)=\left(\sqrt{-x^2+4x+21}-\sqrt{-x^2+3x+10}\right)}}$\\\\ Ans:\Rightarrow ::::=\sqrt{2} ...

$\textbf{Calculate value of $\mathbf{x}$ in $}\\\\ \mathbf{(7x+1)^{\frac{1}{3}}+(-x^2+x+8)^{\frac{1}{3}}+(x^2-8x-1)^{\frac{1}{3}}=2}$ ...

$\textbf{If $\mathbf{x_{1},x_{2},x_{3},.......,x_{n}}$ are the roots of the equation $\mathbf{x^n+2x^{n-1}+3x^{n-2}+.........+nx+n+1=0}$.\\\\ Then Calcuate value of $\mathbf{\sum_{k=1}^{n}\frac{x_{k}^{n+1}-1}{x_{k}-1}=}$ } ...

Find the largest interval in which x lies satisfying x^{12}-x^{9}+x^{4}-x+1>0 ...

What is the largest integer n such that 33! divisible by 2n? ...

If log5k+log35+log1x= 1 then, find the value of x... ...