Question

If x^2+9y^2=369 and xy =16. Find the value of x-3y

Answer 1

Answer:

$( {x - 3y)}^{2} = {x}^{2} + {(3y)}^{2} - 2 \times x \times 3y \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 9 {y}^{2} - 6xy \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 369 - 6 \times 16 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 369 - 96 = 273 \\ x - 3y = \sqrt{273}$