
Example: If x  1/x = 3, find the value of x^{2}+1/x^{2} and x^{4}+1/x^{4}. Solution: Given that, x  1/x = 3 Squaring on both sides, we get (x1/x)^{2} = 3^{2} x^{2}+1/x^{2}2.x^{2}.1/x^{2} = 9 x^{2}+1/x^{2}2 = 9 x^{2}+1/x^{2} = 9+2 x^{2}+1/x^{2} = 11 Squaring on both sides, we get (x^{2}+1/x^{2})^{2} = 11^{2} (x^{2})^{2}+(1/x^{2})^{2}+2.x^{2}.1/x^{2} = 121 x^{4}+1/x^{4}+2 = 121 x^{4}+1/x^{4} = 1212 x^{4}+1/x^{4} = 119. Directions: Solve the following problems. Also write at least five examples of your own. 