Question

compute the value of 9x^2+4y^2 if xy=6 and 3x+2y=12​

Answer 1

hey I am attaching as pic the answer 72

Answer 2

Step-by-step explanation:

Given : Two terms which are $xy=6$  and  $3x+2y=12$

To find : The value of  $9x^{2} +4y^{2}$.

Formula used : We use algebraic identity

$(a+b)^{2} =a^{2} +b^{2} +2ab$

• Finding value of $9x^{2} +4y^{2}$

We have values such as,

⇒ $xy=6$  

⇒ $3x+2y=12$

We start with the algebraic identity where $a=3x$  and $b=2y$.

⇒  $(a+b)^{2} =a^{2} +b^{2} +2ab$

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

               $=9x^{2} +4y^{2} +12xy$

we have to find the value of $9x^{2} +4y^{2}$ ,

⇒  $(3x+2y)^{2}-12xy =9x^{2} +4y^{2}$

by putting values of $(3x+2y )$  and $xy$  we get,

⇒  $9x^{2} +4y^{2}=(12)^{2}-12*6$

                $=144-72$

                $=72$

Hence we get the value of $9x^{2} +4y^{2}$ which is $72$.