Question

If a= 2+ root3 + root5 , b= 3 + root3 - root5, find (a-2)2 + (b-3)2

Answer 1

Given: a =2+ √3 + √5
           b= 3 + √3 -√5
⇒(a-2)2 + (b-3)2
⇒2(a + b) - 10
⇒2(2+ √3 + √5 + 3 + √3 -√5) - 10
⇒-2√3

∴ (a-2)2 + (b-3)2 = -2√3