Ask and Speak Mathematics

 Exercise: Determine the values of $a\And b$ such that ${{\left( \frac{1+\sqrt{5}}{2} \right)}^{12}}=a+b\sqrt{5}$ Solution: Let $u=\fr...

Exercise: Solve in $\mathbb{R}$, 1)       $\sqrt{x}-\left| x-2 \right|<1$ 2)       ${{\sin }^{4}}x+{{\cos }^{4}}x=1$ 3)      ...

Exercise: Evaluate the following $\underset{n\to \infty }{\mathop{\lim }}\,\frac{\sqrt[{{n}^{2}}]{\prod\nolimits_{k=1,2,...,n}{k!}}}{\...

Exercise: Solve in $\mathbb{R}$, $x=\sqrt{21-\sqrt{21+x}}$ Solution: In order to crack this equation we will use zero trick So that, $x=\...

Exercise: Show that, the ratio of AB over BC is golden ratio if an only if the quadrilateral of side $AB$ is square in the right fig...