Question

Q16. Find the values of a and b, if √5-1 + √5+1 = a + b√5 √5+1 √5-1​

Answer 1

Step-by-step explanation:

(b) 4 3 43 a = √ 5 + 1 √ 5 − 1 5+15−1 x √ 5 + 1 √ 5 + 1 5+15+1 = ( √ 5 + 1 ) 2 5 − 1 (5+1)25−1 = 5 + 1 + 2 √ 5 4 = 3 + √ 5 2 5+1+254=3+52 b = √ 5 − 1 √ 5 + 1 5−15+1 x √ 5 − 1 √ 5 − 1 5−15−1 = ( √ 5 − 1 ) 2 5 − 1 (5−1)25−1 = 5 + 1 − 2 √ 5 4 = 3 − √ 5 2 5+1−254=3−52 ∴ a2 + b2 = ( 3 + √ 5 2 ) 2 + (3+52)2+ ( 3 − √ 5 2 ) 2 (3−52)2 = 9 + 5 + 6 √ 5 + 9 + 5 − 6 √ 5 4 = 28 4 = 7 9+5+65+9+5−654=284=7 ab = ( 3 + √ 5 2 ) (3+52) x ( 3 − √ 5 2 ) (3−52) = 9 − 5 4 = 4 4 = 1 9−54=44=1