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What is the answer to 8/z -z=4 in solving rational equations?

2 Answers

6 votes

Explanation:

8-z^2=4z

8-z^2-4z=0

-z^2-4z+8=0

z^2+4z-8=0

z(z+4)=8

{{z==-5.46410161514},{z==1.46410161514}}

User Stef
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8.2k points
2 votes

Start with


(8)/(z)-z=4

Note that this implies that z cannot be zero, otherwise in the term 8/z you would have a division by zero.

So, supposing that z is not zero, we multiply both sides by z:


8-z^2=4z

Rearrange the equation into


z^2+4z-8=0

And solve the quadratic equation as usual to get


z = (-4\pm√(16+32))/(2) = (-4\pm√(48))/(2)= (-4\pm4√(3))/(2) = -2\pm2√(3)

Since both of these solutions are non-zero, we can accept them.

User Pradyuman
by
8.2k points

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