Question

Let 'a' and 'b' be the roots of x^2-5x+3 with a>b . If ,tn= a^n - b^n for n>0, then find the value of (t8+3t6)/t7.

Answer 1

Given 'a' and 'b' be the roots of x^2-5x+3 with a>b . If ,tn= a^n - b^n for n>0,

Now solving the quadratic equation we get

a = (5 + √13)/2 and b = (5 - √13)/2

Now put the values of a and b in the equation tn and get the value