
Example: If x+y = 9 and xy = 18, find the value of x^{4}+y^{4}. Solution: Given that, x+y = 9 Squaring on both sides, we get (x+y)^{2} = 9^{2} x^{2}+y^{2}+2xy = 81 x^{2}+y^{2}+2.18 = 81 x^{2}+y^{2}+36 = 81 x^{2}+y^{2} = 8136 x^{2}+y^{2} = 45 Squaring on both sides, we get (x^{2}+y^{2})^{2} = 45^{2} (x^{2})^{2}+(y^{2})^{2}+2.x^{2}y^{2} = 2025 x^{4}+y^{4} + 2.18.18 = 2025 x^{4}+y^{4}+648 = 2025 x^{4}+y^{4} = 2025648 x^{4}+y^{4} = 1377 Directions: Solve the following problems. Also write at least five examples of your own. 