1

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

\$ ((5x)^2 + (4y)^2)/(xy) = -40 \$

2

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

\$ ((5x)^2 + (4y)^2) = -40(xy) \$

3

After simplification we get

\$ (5x)^2 +40xy + (4y)^2 = 0 \$

4

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

\$ (5x + 4y)^2 = 0 \$

5

Applying squareroot on both sides we get

\$ \sqrt(5x + 4y)^2 = \sqrt0 \$

6

Cancelling Square & Squareroot we get

\$ (5x + 4y) = 0 \$

7

Moving "\$ 4y \$" to left side we get

\$ (5x = -4y) \$

8

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

\$ 5x = -4y \$
\$ 5x/y=-4 \$
\$ x/y=-4/5 \$

9

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

\$ x/y=-4/5 \$

10

Answer

D = \$ x/y = -4/5 \$