If 5 /( 4√2 )+ (3+2√2) / (3−2√2) − (3−2√2) /(3+2√2) = a + b √2, then what is the value of (3a + 4b)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 98½
Concept
Rationalization
a2 - b2 = ( a + b) ( a - b)
5 / 4√2 × √2 / √2 = 5√2 / 8
(3+2√2) / (3−2√2) × ( 3+2√2) / (3+2√2) =17+12√2
(3 - 2√2) / (3 + 2√2) × ( 3 - 2√2) / (3 - 2√2) =17 - 12√2
According to the question
5√2 / 8 + 17+12√2 + 17 - 12√2 = a + b √2
0 + 197√2 / 8 = a + b√2
On comparing
a = 0
b = 197 / 8
(3a + 4b) = 3 × 0 + 4 × 197/8 = 197/2 = 98½