Question

15. If x + 2y = 9 and xy = 7, find the value of x2 + 4y2​

Answer 1

Given,

x + 2y = 9 and xy = 7

To find,

x² + 4y²

Solution,

Since, xy = 7

x = 7/y

• Now, putting x = 7/y in the equation x + 2y = 9 we get,

⇒   7/y +2y =9

⇒   7 + 2y² = 9y

⇒   2y² - 9y + 7 = 0

Factorizing we get,

⇒   2y²-7y-2y+7=0

⇒   y(2y-7)-(2y-7)=0

⇒   y-1=0 and 2y-7=0

⇒   y =1 and y =7/2

• So, xy=7   x(1)=7 , we get x = 7 and y =1 and x(7/2)=7 we get x=2 and y=7/2

Therefore, the value of x² + 4y² is-

⇒   (7)²+4(1)² = 49 + 4 = 53

⇒   (2)²+4(7/2)² = 53.

Therefore, if x + 2y = 9 and xy = 7, find the value of x²+ 4y² is 53.