If 2x + y = 15 and xy = 18, then the value of (4x² - y²)

Solution

ATQ, We know that, (a- b)² = (a + b2 - 4ab So, (2x - y)² = (2x + y)2 - 4 × 2xy = 152 - 8 × 18 = 225 - 144 = 81 So, we can say that, (2x - y) = - 9, or, 9. Since, all the given options are positive, so we will consider the positive value of (2x - y) , as (2x + y) is given positive. We know that, a2 - b² = (a + b) × (a - b) So, 4x² - y² = (2x)2  - y2 = (2x + y) × (2x - y) = 15 × 9 = 135 Alternate solution Through trial and error, we can observe that x = 6 and y = 3. So, required value = {4 × (6)2 - 32 } = (4 × 36) - 9 = 135