Question

Alpha ^4+beta ^4=____________

Answer 1

α^4 + β^4

=> (α²)² + (β²)²

=> (α² + β²)² - 2α²β²        by using a² + b² = (a + b)² - 2ab

=> ((α + β)²  - 2αβ)² - 2(αβ)²        using the same identity again


We will now substitute the values of α + β and αβ we found in the beginning of the solution


=> ((-b/a)² - 2c/a)² - 2(c/a)²

=> (b²/a² - 2c/a)² - 2c²/a²

=> ((b² - 2ac)/a²)² - 2c²/a²

=> (b² - 2ac)²/a⁴ - 2c²/a²

=> ((b² - 2ac)² - 2a²c²) / a⁴
=> (b⁴ - 4ab²c + 4a²c² - 2a²c²) / a⁴

=> (b⁴ - 4ab²c + 2a²c²) / a⁴