2010 · Q27
If α and β are the roots of the equation x² - x - 1 = 0, then what is the value of (α⁴ + β⁴) ?
Elementary MathematicsAlgebra
- A7
- B0
- C2
- DNone of the above
Explanation
α+β=1, αβ=-1; α⁴+β⁴=((α+β)²-2αβ)²-2(αβ)²=7.
If α and β are the roots of the equation x² - x - 1 = 0, then what is the value of (α⁴ + β⁴) ?
Explanation
α+β=1, αβ=-1; α⁴+β⁴=((α+β)²-2αβ)²-2(αβ)²=7.