If x - 2y = 3 and 2xy = 5, then find the value of (x + 2y)2.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 29
Given:
x - 2y = 3 and
2xy = 5
⇒ xy = 5/2
(x - y)2 = x2 + y2 - 2xy
(x + y)2 = x2 + y2 + 2xy
Explanation:
According to the given question,
(x - 2y)2 = 9
⇒ x2 + 4y2 - 4xy = 9
⇒ x2 + 4y2 = 9 + 4xy
⇒ x2 + 4y2 = 9 + 4 × (5/2)
⇒ x2 + 4y2 = 9 + 10
⇒ x2 + 4y2 = 19
Now, (x + 2y)2 = x2 + 4y2 + 4xy
⇒ (x + 2y)2 = 19 + 4 × (5/2)
⇒ (x + 2y)2 = 29
Hence the required answer is 29.