Solve the equation

x^2(1+x)^2+x^2=8(1+x)^2

Compute the smallest positive integer n for which

\sqrt{100+\sqrt{n} } +\sqrt{100-\sqrt{n} }

is an integer

Exact Trigonometric Values from 1° to 90°

If a_1=1, a_{n+1}=a_n+n(n+1), find the formula for general terms of the sequence.

Determine the value of \sin 36\degree

Find the exact value of sin 33\degree

Solve the cube root equation

\sqrt[3]{14+\sqrt{x} } +\sqrt[3]{14-\sqrt{x} } =4

Show the rule of the divisibility for 4

Show the rule of the divisibility for 3

Determine the value of cos⁡1110°

Solve the equation

(x+2)^4+(x+1)^4=97