Question

if aplha and beta are roots of equation x^2-x-1 =0 then alpha^4+ beta^4=?​

Answer 1

Answer:

Step-by-step explanation:

x² - x - 1 = 0

a = 1, b = -1, c = -1

Sum of roots = α + β = -b/a = -(-1)/1 = 1

Product of roots = αβ = c/a = -1/1 = -1

//Also we know that a² + b² = (a + b)² - 2ab

α⁴ + β⁴ =  (α²)² + (β²)² = (α² + β²)² - 2α²β²

             = [(α + β)² - 2αβ]² - 2(αβ)²

             = [(1)² - 2(-1)]² - 2(-1)²

             = (1 + 2)² - 2

              = 9 - 2

               = 7.