Algebra and Applications Test 3

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Question : 7 of 25

Marks: +1, -0

If

f + g + h = 0

, then what is the value of

f ^4 + g^4 + h^4 - 2f ^2 g^2 - 2g^2 h^2 - 2h^2 g^2

?

0
1
-1
$1/ 2$
None of these

Solution:

Given that,

f + g + h = 0

f ^4 + g^4 + h^4 - 2f ^2 g^2 - 2g^2 h^2 - 2h^2 g^2

= (f ^2 - g^2 ) ^2 h^4 - 2h^2 (f ^2 + g^2 )

= (f ^2 + g^2 ) ^2 + h^4 - 2h^2 (f^ 2 + g^2 ) - 4f^ 2 g^2

= (f ^2 + g^2 - h^2 ) ^2 - 4f^ 2 g^2

= (f + g^2 ) ^2 - 2fg - h^2 ) - 4f ^2 g^2

= (h^2 - 2fg - h^2 ) ^2 - 4f ^2 g^2

= 4f^ 2 g^2 - 4f ^2 g^2 = 0

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