Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
for what value of m, x4+4x2+m+8/x2+4/x4 is a complete square where x is not equal to 0Asked by ayisha
for what value of m, x4+4x2+m+8/x2+4/x4 is a complete square where x is not equal to 0
Answers
Answered by
Steve
x^4 + 4x^2 + m + 8/x^2 + 4/x^4
well, we will have
(x^2 + k + 2/x^2)^2
x^4 + kx^2 + 2 + + kx^2 + k^2 + 2k/x^2 + 2 + 2k/x^2 + 4/x^4
x^4 + 2kx^2 + 4 + k^2 + 4k/x^2 + 4/x^4
equate like powers of x to find that we must have k=2
so m = 4+k^2 = 8
well, we will have
(x^2 + k + 2/x^2)^2
x^4 + kx^2 + 2 + + kx^2 + k^2 + 2k/x^2 + 2 + 2k/x^2 + 4/x^4
x^4 + 2kx^2 + 4 + k^2 + 4k/x^2 + 4/x^4
equate like powers of x to find that we must have k=2
so m = 4+k^2 = 8
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.