Algebra and Applications Test 2

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Question : 13 of 40

Marks: +1, -0

If

c^4 + d^4 = 17

and

c + d = 1

, what is the value of c

^2 d^2 - 2cd

?

8
10
12
16
None of these

Solution:

Since,

c^ 4 + d^4 = 17

and

c + d = 1

Now,

(c + d)^ 2 = 1

⇒c^2+d^2+2cd=1

⇒(c^2+d^2+2cd)^2=1

⇒c^4+d^4+4c^2d^2+2c^2d^2+4cd^2+4c^3d=1

⇒17+6c^2d^2+4cd(c^2+d^2)=1

⇒1 7+6c^2d^2+4cd(1-2cd)=1

⇒17+6c^2d^2+4cd-8c^2d^2=1

⇒16=2c^2d^2-4cd

⇒c^2d^2-2cd=8

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