If p = and q = , then find p 2 + q 2 .

Step-by-step solution

Given p = Multiplying and dividing R.H.S. by , we get p = = and q = (Rationalising the denominator) On solving, we get q = 5 + 2 Now, pq = (5 – 2 ) (5 + 2 ) = (5) 2 − (2 ) 2 = 25 – 24 = 1 and p + q = 5 – 2 + 5 + 2 = 10 Now, ( p + q ) 2 = 10 2 p 2 + q 2 + 2 pq = 100 p 2 + q 2 + 2 × 1 = 100 p 2 + q 2 = 100 – 2 = 98