Question

√15-1/√15+1+√15+1/√15-1=a+b√15.find the values of a and b

Answer 1

Sol: We know that (√a+√b)2 = a+b+2√ab Now √(5 + 2√6). If it is a perfect sq, there will be 2 no.s - such that a + b = 5. 2√ab = 2√6 ⇒ ab = 6 (a=3, b=2) so that, 5 + 2√6 = 3+2+2√(3×2) =(√3+√2)2 ∴ √( 5 + 2√6) = √3+√2. similarly, Consider √(8 - 2√15) a + b = 8 ⇒ ab = 15 (a = 5,b = 3) √(8 - 2√15) = (√5 - √3) Now √( 5 + 2√6) + √(8 - 2√15) = √3 + √2 + √5 - √3 = √2 + √5.