Can we Find any two Distinct Functions
$$ f:\Re \rightarrow \Re $$ such that
$$ f\left ( x \right )=f\left (\frac{x}{2}\right ) $$
$$ f:\Re \rightarrow \Re $$ such that
$$ f\left ( x \right )=f\left (\frac{x}{2}\right ) $$
Thursday 18 April 2013
Necessary and Sufficient Conditions for the General Second Degree Equation
$$ Ax^2+2Hxy+By^2+2Gx+2Fy+C=0 $$
to Represent Pair of Straight Lines:
$$
\Delta =\begin{vmatrix}
A & H &G\\
H& B & F\\
G& F& C
\end{vmatrix} =0
$$
Case 1 :if $$ H^2 > AB $$ Then they are Intersecting pair of Straight Lines
Case 2: if $$ H^2 = AB $$ Then they are pair of Parallel Straight Lines
Case 3: if $$ H^2 < AB $$ Then they Represent a Point in a Plane
$$ Ax^2+2Hxy+By^2+2Gx+2Fy+C=0 $$
to Represent Pair of Straight Lines:
$$
\Delta =\begin{vmatrix}
A & H &G\\
H& B & F\\
G& F& C
\end{vmatrix} =0
$$
Case 1 :if $$ H^2 > AB $$ Then they are Intersecting pair of Straight Lines
Case 2: if $$ H^2 = AB $$ Then they are pair of Parallel Straight Lines
Case 3: if $$ H^2 < AB $$ Then they Represent a Point in a Plane
Friday 8 February 2013
Remainder Problem
Find the Remainder when the number $N$ is divided by 7, where
$$ N=2222^{5555}+5555^{2222} $$
$$ N=2222^{5555}+5555^{2222} $$
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