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

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

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

Answers (1)

Consider the equation,
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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