# explain how you can tell from the form of the equation 1/2z^2=-3 that it has no solution.

Question
explain how you can tell from the form of the equation $$\displaystyle\frac{{1}}{{2}}{z}^{{2}}=-{3}$$ that it has no solution.

2021-03-10
Consider the equation,
$$\displaystyle\frac{{1}}{{{2}{z}^{{2}}}}=−{3}$$
Left hand side $$\displaystyle=\frac{{1}}{{{2}{z}^{{2}}}}$$ and Right hand side = - 3.
From above equation,
Left hand side $$\displaystyle=\frac{{1}}{{{2}{z}^{{2}}}}$$ is always positive for any values of z.
Fight hand side = -3 is negative .
To get,
Left hand side is not equal to the right hand side.
Since left hand side is always positive for any values of z except if z is zero or undefined , it can be never equal a negative number and right hand side is negative. Then,
The equation $$\displaystyle\frac{{1}}{{{2}{z}^{{2}}}}=−{3}$$ has no solution.

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