Question

If 2x + 3y =8 and xy = 4 then find the value of 4x²+9y²​

Answer 1

Step-by-step explanation:

$( {2x + 3y})^{2} = 4 {x}^{2} + 9 {y}^{2} + 12xy \\ ( {8})^{2} = 4 {x}^{2} + 9 {y}^{2} + 12 \times 4 \\ 64 = 4 {x}^{2} + 9 {y}^{2} + 48 \\ 64 - 48 = 4 {x}^{2} + 9 {y}^{2} \\ 16 = 4 {x}^{2} + 9 {y}^{2} \\ 4 {x}^{2} + 9 {y}^{2} = 16$