Question

if x^2 + 9y^2 =9 and xy= 1 find (2x+6y)^2​

Answer 1

Answer:

${x}^{2} + {(3y)}^{2} = 9$

${(x + 3y)}^{2} - 2x \times 3y = 9$

${(x + 3y) }^{2} - 6xy = 9$

Since, X Y = 1

Therefore,

${(x + 3y) }^{2} - 6 = 9$

${(x + 3y)}^{2} = 15$

$x + 3y = \sqrt{15}$

$2(x + 3y) = 2 \sqrt{15}$

$2x + 6y = 2 \sqrt{15}$

${(2x + 6y)}^{2} = {(2 \sqrt{15)} }^{2}$

${(2x + 6y) }^{2} = 60$

Hope it helps you.....