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Algebra and Applications Test 2

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Question : 13 of 40

Marks: +1, -0

If

c^4 + d^4 = 17

c + d = 1

, what is the value of c

c^2 d^2 - 2cd

?

8
10
12
16
None of these

Solution: 👈: Video Solution

Concept:

Use the symmetric sum substitution

s=cd

and relate

c^4+d^4

to

s

.

Explanation:

Given

c+d=1

, we have

(c+d)^2=c^2+d^2+2cd=1

.

So

c^2+d^2=1-2cd

.

Let

s=cd

.

Then

c^2+d^2=1-2s

.

Now

c^4+d^4=(c^2+d^2)^2-2c^2d^2

.

Substitute

c^4+d^4=17

and

c^2d^2=s^2

:

17=(1-2s)^2-2s^2

.

Simplify:

17=1-4s+4s^2-2s^2=1-4s+2s^2

.

Thus

2s^2-4s-16=0

.

Dividing by

2

gives

s^2-2s=8

.

The required expression is

c^2d^2-2cd=s^2-2s=8

.

Answer:

The value is

8

, so the correct option is A.

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