Question

If a = 5 +2√6 and b = 1/a, then find the values of: (i) a2+b2 (ii)a3+b3 ​

Answer 1

Step-by-step explanation:

Here a= 5 +2√6

b= 1/a

=> 1/ (5+2√6)

=> ( 5-2√6) / (5+2√6) (5-2√6)

=> (5-2√6) / {5²-- ( 2√6)²}

=> (5-2√6) / 25-24

=> 5-2√6

now, a²+b²= (a+b)²- 2ab

=> (5+2√6+5-2√6)² - 2(5–2√6) (5–2√6)

=> (10)²–2 (25–24)

=> 100–2

=> 98

: Hence, a²+b²= 98