Question

Hello !
$a = \frac{ \sqrt{2x + 3y} }{2x + 3y} \frac { \sqrt { 2x - 3y} }{2x - 3y}$
find
$3y {a}^{2} - 4xa + 3y$

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Answer 1

Step-by-step explanation:

Begin with x2 + xy + y2 = 1 . Differentiate both sides of the equation, getting

D ( x2 + xy + y2 ) = D ( 1 ) ,

2x + ( xy' + (1)y ) + 2 y y' = 0 ,

so that (Now solve for y' .)

xy' + 2 y y' = - 2x - y ,

(Factor out y' .)

y' [ x + 2y ] = - 2 x - y ,

and the first derivative as a function of x and y is

(Equation 1)

 .

To find y'' , differentiate both sides of this equation, getting







 .

Use Equation 1 to substitute for y' , getting



(Get a common denominator in the numerator and simplify the expression.)







 .

This answer can be simplified even further. Note that the original equation is

x2 + xy + y2 = 1 ,

so that

(Equation 2)

x2 + y2 = 1 - xy .

Use Equation 2 to substitute into the equation for y'' , getting

Answer 2

$\huge\bf{Answer:-}$

Refer the attachments.