Quadratic Equations
You went on a 360km train ride but you are late! If the train had just been 5 km/hr faster, then the train ride would have been one hour shorter.
How fast was the train going?
by
Abu Bakar Khan
If \(a\) and \(b\) are non-zero real numbers, simplify: \[\left(a + \frac1a\right)^2+\left(b + \frac1b\right)^2 + \left(ab + \frac1{ab}\right)^2 \\ - \left(a + \frac1a\right)\left(b + \frac1b\right)\left(ab + \frac1{ab}\right) \]
by
madhav srirangan
\[ x(x+1)(x+2)(x+3)=120\]
Find the sum of all the real roots of the equation above.
by
Sandeep Bhardwaj
\[\large (x^2 - 5x + 5)^{(x^2 - 11x + 30)} = 1\]
How many different integers satisfy the equation above?
by
Sharky Kesa
How many real value(s) of \(x\) exist satisfy the equation \[ \left( 5+2\sqrt{6} \right)^{x^2-3}+\left( 5-2\sqrt{6} \right)^{x^2-3}=10 ? \]
by
Sandeep Bhardwaj