Let α and β be the roots of the equation x 2 - x - 1 = 0 . If p k = α k + β k , k ≥ 1 , then which one of the following statements is not true?

Question

Let &#945; and &#946; be the roots of the equation x 2 - x - 1 = 0 . If p k = &#945; k + &#946; k , k &#8805; 1 , then which one of the following statements is not true?

Aicharya · Accepted Answer

&#945; 5 = 5 &#945; + 3 &#946; 5 = 5 &#946; + 3 P 5 = 5 &#945; + &#946; + 6 = 5 1 + 6 P 5 = 11 and P 2 = &#945; 2 + &#946; 2 = &#945; + 1 + &#946; + 1 = 3 and P 3 = &#945; 3 + &#946; 3 = 2 &#945; + 1 + 2 &#946; + 1 = 2 1 + 2 = 4 P 2 &#215; P 3 = 12 and P 5 = 11 &#8658; P 5 &#8800; P 2 &#215; P 3

Let α and β be the roots of the equation x 2 - x - 1 = 0 . If p k = α k + β k , k &#8805…

Solution

Let &#945; and &#946; be the roots of the equation x 2 - x - 1 = 0 . If p k = &#945; k + &#946; k , k &#8805…

Solution

Let α and β be the roots of the equation x 2 - x - 1 = 0 . If p k = α k + β k , k &#8805…