Find largest positive value of $n$ in $ n.\left(\frac{abc}{ab+bc+ca}\right)\leq (a+b)^2+(a+b+4c)^2$
where $a\;,b\;,c\in\mathbb{R}$
Search found 38 matches
- Thu Nov 10, 2011 10:21 pm
- Forum: Algebra
- Topic: Largest value of n
- Replies: 0
- Views: 1632
- Thu Nov 10, 2011 10:18 pm
- Forum: Algebra
- Topic: nested roots
- Replies: 0
- Views: 1657
nested roots
find value of $\left(2+\sqrt{1+\sqrt{2+\sqrt{1+\sqrt{2+...}}}}\right)-\left(1+\sqrt{2+\sqrt{1+\sqrt{2+\sqrt{1+...}}}}\right)=$
- Thu Jun 02, 2011 9:46 pm
- Forum: Algebra
- Topic: Range of f(x) (2)
- Replies: 0
- Views: 1639
Range of f(x) (2)
If $a^2+c^2>ab$ and $b^2>4c^2$ for all $x\in \mathbb{R}$
then Range of $\displaystyle f(x) = \frac{x+a}{x^2+bx+c^2}$
then Range of $\displaystyle f(x) = \frac{x+a}{x^2+bx+c^2}$
- Thu Jun 02, 2011 9:43 pm
- Forum: Algebra
- Topic: minimum value
- Replies: 4
- Views: 3343
Re: minimum value
Here Domain is $x\in\mathbb{R}-\left\{-1\right\}$
- Sat May 28, 2011 3:04 pm
- Forum: Algebra
- Topic: minimum value
- Replies: 4
- Views: 3343
minimum value
Calculate minimum value of $\displaystyle f(x)=\frac{x^4+x^2+1}{(x+1)^2}$
Without using calculus
Without using calculus
- Sat May 28, 2011 2:56 pm
- Forum: Number Theory
- Topic: Find the real value of (x,y)
- Replies: 4
- Views: 3102
Re: Find the real value of (x,y)
Here $\mathbf{(4x^2+6x+4).(4y^2-12y+25)=28}$
$\mathbf{\left\{(x+\frac{3}{4})^2+\frac{7}{16}\right\}.\left\{(y-\frac{3}{2})^2+\frac{16}{4}\right\}=\frac{7}{4}}$
Which is possiable only when $\mathbf{x=-\frac{3}{4}}$ and $\mathbf{y=\frac{3}{2}}$
$\mathbf{\left\{(x+\frac{3}{4})^2+\frac{7}{16}\right\}.\left\{(y-\frac{3}{2})^2+\frac{16}{4}\right\}=\frac{7}{4}}$
Which is possiable only when $\mathbf{x=-\frac{3}{4}}$ and $\mathbf{y=\frac{3}{2}}$
- Wed Apr 13, 2011 7:37 pm
- Forum: Higher Secondary Level
- Topic: limit with fractional part
- Replies: 4
- Views: 3574
Re: limit with fractional part
No It is $ = 1$
- Fri Apr 08, 2011 5:11 pm
- Forum: Higher Secondary Level
- Topic: limit with fractional part
- Replies: 4
- Views: 3574
limit with fractional part
Calculate $\lim_{n \to \infty} \left\{\left(\sqrt{3}+1\right)^{2n} \right\} =$
Where $\left\{.\right\} =$fractional part function
Where $\left\{.\right\} =$fractional part function
- Wed Mar 23, 2011 6:33 pm
- Forum: Algebra
- Topic: no. of zeros
- Replies: 3
- Views: 2725
Re: no. of zeros
Thanks babai
- Wed Mar 23, 2011 6:33 pm
- Forum: Algebra
- Topic: Polynomial equation
- Replies: 5
- Views: 4146
Re: Polynomial equation
Now How can I Calculate other Roots.