1

Find the postive value of \$ x/y\$

\$ (16x^2 + 9y^2)/(xy) = 24 \$

2

Moving "\$ xy \$" to left side we get

\$ (16x^2 + 9y^2) = 24(xy) \$

3

After simplification we get

\$ 16x^2 - 24xy + 9y^2 = 0 \$

4

Using identity \$a^2 - 2ab + b^2 = (a - b)^2\$, we get

\$ (4x - 3y)^2 = 0 \$

5

Applying squareroot on both sides we get

\$ \sqrt(4x - 3y)^2 = \sqrt0 \$

6

Cancelling Square & Squareroot we get

\$ (4x - 3y) = 0 \$

7

Moving "\$ -3y \$" to left side we get

\$ (4x = 3y) \$

8

Transforming the above equation into \$ x/y \$ form, we get

\$ 4x = 3y \$
\$ 4x/y=3 \$
\$ x/y=3/4 \$

9

The positive valve of "\$ x/y \$" is

\$ x/y=3/4 \$

10

Answer

A = \$ x/y = 3/4 \$