If #8sqrt(4z^2 - 43) = 40#, what is the value of #z#?
Assumption: the question is:
This is done in stages. First you have all the terms with z on the LHS of = and all the terms without z on the other side. Then you manipulate the LHS side until the only thing left is the single z.
Add 43 to both sides giving
Taking the root
Thus LHS=RHS so
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Isolate the square-root.
Checking in the original equation, both solutions work.
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To solve for ( z ):
[ 8\sqrt{4z^2 - 43} = 40 ]
[ \sqrt{4z^2 - 43} = 5 ]
[ 4z^2 - 43 = 5^2 ]
[ 4z^2 - 43 = 25 ]
[ 4z^2 = 25 + 43 ]
[ 4z^2 = 68 ]
[ z^2 = \frac{68}{4} ]
[ z^2 = 17 ]
[ z = \pm \sqrt{17} ]
So, the possible values of ( z ) are ( z = \sqrt{17} ) and ( z = -\sqrt{17} ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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