Question

Compute the value of 9x2 + 4y2 if xy = 6 and 3x + 2y = 12.​

Answer 1

✵Given:✵

⇒ Compute the value: 9x² + 4y² if xy = 6 and 3x + 2y = 12.

Calculations:

We know that, the give equation is:

⇒$\sf 3x + 2y = 123x+2y=12$

We have to square both the sides:

⇒$\sf 3x + 2y^2 = 12^23x+2y$

⇒ $\sf 9x^2 + 12xy + 4y^2 = 1449x$

⇒$\sf 9x^2 + 4y^2 = 144 - 12xy^9x$

Taking, (xy = 6):

⇒ $\sf 9x^2 + 4y^2 = 144 - 729x$

⇒${\sf{\underline{\boxed{\red{\sf{ 9x2 + 4y2 = 72}}}}}}$

✯This is the required answer:✯

Answer 2

⇒ Compute the value: 9x² + 4y² if xy = 6 and 3x + 2y = 12.

Calculations:

We know that, the give equation is:

⇒\sf 3x + 2y = 123x+2y=123x+2y=123x+2y=12

We have to square both the sides:

⇒\sf 3x + 2y^2 = 12^23x+2y3x+2y²

=12² 3x+2y

\sf 9x^2 + 12xy + 4y^2 = 1449x9x² +12xy+4y²

=1449x

9x^2 + 4y^2 = 144 - 12xy^9x9x²+4y²

=144−12xy9x

Taking, (xy = 6):

⇒9x^2 + 4y^2 = 144 - 729x9x²+4y²

=144−729x

$⇒{\sf{\underline{\boxed{\red{\sf{ 9x2 + 4y2 = 72}}}}}} </p><p>9x2+4y2=72$