Question

z^2/Z^2-64=-8 evaluate for the given value of the variable

Answer 1

How do I cross muliply

Answer 2

Is the left hand side:
\[\frac{z^2}{z^2-64}\]?

Answer 3

yes

Answer 4

Multiply both sides of the question by \(z^2-64\) to get:
\[z^2=-8(z^2-64)\]
Can you then expand the brackets on the right hand side and tell me what you get?

Answer 5

muliply 64 by 8

Answer 6

Yes, don't forget to multiply \(z^2\) by -8 as well. You will get:
\[z^2=-8z^2+512\]
Now we can combine all \(z^2\) terms on the left hand side to get:
\[9z^2=512\]
Then divide by 9 to get:
\[z^2=\frac{512}{9}\]
And hence \(z=\sqrt{\frac{512}{9}}\) which if you simplify is \(z=\frac{16\sqrt{2}}{3} \)
Do you understand?

Answer 7

When I got it I got 512/9 and put it in and they said it was wrong.

Answer 8

did you take the square root
btw, you get ± (two answers)

Answer 9

I cannot read the one where it was simplify

Answer 10

\[z=\pm \sqrt{\frac{512}{9}}=\pm\frac{16\sqrt{2}}{3} \]
The last part is the bit after the simplify.

Answer 11

thanks I will try it