
Example: If x + 1/x = 5, find the value of x^{2}+1/x^{2} and x^{4}+1/x^{4}. Solution: Given that, x + 1/x = 5 Squaring on both sides, we get (x+1/x)^{2} = 5^{2} x^{2}+1/x^{2}+2.x^{2}.1/x^{2} = 25 x^{2}+1/x^{2}+2 = 25 x^{2}+1/x^{2} = 252 x^{2}+1/x^{2} = 23 Squaring on both sides, we get (x^{2}+1/x^{2})^{2} = 23^{2} (x^{2})^{2}+(1/x^{2})^{2}+2.x^{2}.1/x^{2} = 529 x^{4}+1/x^{4}+2 = 529 x^{4}+1/x^{4} = 5292 x^{4}+1/x^{4} = 527. Directions: Solve the following problems. Also write at least five examples of your own. 