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Algebra and Applications Test 3

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Question : 6 of 25

Marks: +1, -0

If

v + \frac{1}{w} = 1

4 + \frac{1}{v} = 1

what is the value of

uvw

?

1
-1
0
$\frac{1}{2}$
None of these

Solution:

Concept:

Express

u

and

w

in terms of

v

using the two equations, then multiply.

Explanation:

From

v+\frac{1}{w}=1

, we get

\frac{1}{w}=1-v

, so

w=\frac{1}{1-v}

.

From

u+\frac{1}{v}=1

, we get

\frac{1}{v}=1-u

, so

u=\frac{v-1}{v}

.

Now compute

uvw

:

uvw = \left(\frac{v-1}{v}\right) \cdot v \cdot \left(\frac{1}{1-v}\right)

= \frac{v-1}{1-v} = -1

Answer:

The value of

uvw

is

-1

, so the correct option is B.

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