Question

If 3x-2y=8 and xy=5 find the value of 9x²+4y²

Answer 1

Answer:  $9x^{2} +4y^{2} =124$

Step-by-step explanation:

Given, 3x-2y=8, xy=5

To find: 9x²+4y²

• We have, 3x-2y=8. We are expected to find the value of 9x²+4y².

• The hint we get from the question is, by observing that on squaring 3x-2y=8 we get 9x²+4y² as a part of it.

Let us use, $(a-b)^{2} =a^{2} + b^{2} -2ab$ on 3x-2y=8

Clearly, a=3x, b=2y

                                    $(3x-2y)^{2} =8^{2}$

           $(3x)^{2} + (2y)^{2} -2*3x*2y = 8^{2}$

                         $9x^{2}+4y^{2}-12xy=64$      

Given the value of xy=5,

On substituting we get,

                           $9x^{2}+4y^{2}-12*5=64$

                                 $9x^{2}+4y^{2}-60=64$

                                 $9x^{2}+4y^{2}=64+60$

                                $9x^{2}+4y^{2}=124$

∴ The value of 9x²+4y²=124

 

 

(#SPJ3)

Answer 2

The value of $9x^{2}$+$4y^{2}$ is 12xy+ 64.

Step-by-step explanation:

The Equations given to us are:

3x-2y= 8

xy=5

We need to find the value of 9x²+4y²

Solution:

We know that

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

Squaring 3x-2y, we get

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

$8^{2}$ =$9x^{2}$+$4y^{2}$ -12xy

64=$9x^{2}$+$4y^{2}$ -12xy

so, the value of=$9x^{2}$+$4y^{2}$ is:

$9x^{2}$+$4y^{2}$=  12xy+64

Result:

Thus, the value of $9x^{2}$+$4y^{2}$ is 12xy+ 64.

(#SPJ3)