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How do you solve $y + \frac{9}{y} = 0$ $y+9/y = 0$ ?

1 Answer

May 18, 2018

There is no Real solution (although a Complex solution is possible)

Explanation:

Given
$XXX y + \frac{9}{y} = 0$ $color(white)("XXX")y+9/y=0$

Multiply everything (on both sides) by $y$ $y$
$XXX y^{2} + 9 = 0$ $color(white)("XXX")y^2+9=0$

$XXX y^{2} = - 9$ $color(white)("XXX")y^2=-9$

Since any Real number squared is greater than or equal to zero;
there is no Real solution.

If Complex values are allowed
$XXX y = \pm 3 i$ $color(white)("XXX")y=+-3i$

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