If 2x + 5y = 15 and xy = 6, then the value of 4x2 + 25y2 is ____________.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 105.
xy = 6
2x + 5y = 15
⇒ (2x + 5y)2 = 152 = 225
⇒ 4x2 + 2 × 2x × 5y + 25y2 = 225
⇒ 4x2 + 20xy + 25y2 = 225
⇒ 4x2 + 20 × 6 + 25y2 = 225
⇒ 4x2 + 120 + 25y2 = 225
⇒ 4x2 + 25y2 = 225 - 120 = 105
Therefore, the value of the expression is 105.