Question

4x^2 + 9y^2 = 40 and xy=2 find 2x + 3y

Answer 1

Given, (2x + 3y)

On squaring we get

(2x+3y)^2 = 4x^2 + 9y^2 + 12xy

                 = 40 + 12(2)
 
                 = 40 + 24

                 = 64.


(2x + 3y) = 8.


Hope this helps!

Answer 2

4x² + 9y² = 40 .
xy = 2 .

Now, we know that ( a + b )² = a² + 2ab + b² .

So , ( 2x + 3y )² = ( 2x )² + ( 2.2x.3y ) + ( 3y )²
=> ( 2x + 3y )² = 4x² + 9y² + 12xy
Putting the values of 4x² + 9y² and xy , we get

( 2x + 3y )² = 40 + 12 * 2
=> ( 2x + 3y )² = 64 .
=> ( 2x + 3y ) = 8 . [ Answer ]

Hope it helps !!