If 2a + b = 10, 2ab = 9, and 2a > b, then find the value of 2a – b.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8
Given:
2a + b = 10, 2ab = 9
Formula used:
(a + b)2 = a2 + b2 + 2ab ---- (1)
(a - b)2 = a2 + b2 - 2ab ---- (2)
Calculations:
Using equation (1), we get
⇒ (2a + b)2 = 4a2 + b2 + 2 × 2ab
⇒ 100 = 4a2 + b2 + 18
⇒ 4a2 + b2 = 82
Using equation (2),
⇒ (2a - b)2 = 4a2 + b2 - 18
⇒ (2a - b)2 = 82 - 18
⇒ (2a - b)2 = 64
⇒ (2a - b) = 8