Question

If a = 4-√15 , find a²+1/a²​
Answer please ​

Answer 1

Answer:

Step-by-step explanation:

a = 4 - √15

1/a = 1/4 - √15

//rationalizing by multiplying 4 + √15 in numerator and denominator

      = 1/4 - √15   * 4 + √15 / 4 + √15

      = 4 + √15 / (4 - √15)(4 + √15)

       = 4 + √15 / (4)² - (√15)²

       = 4 + √15 / 16 - 15

        = 4 + √15

So,

a + 1/a = 4 - √15 + 4 + √15 = 8

=> a + 1/a = 8

squaring on both sides

(a + 1/a)² = 8²

=> a² + 2(a)(1/a) + 1/a² = 64

=> a² + 1/a² + 2 = 64

=> a² + 1/a²  = 64 - 2 = 62