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For the expression (√(2x²+1)+√(2x²-1))⁶+ ((2)/(√(2x²+1)+√(2x²-1)))⁶, the degree of the resulting polynomial is:

1. 5
2. 6
3. 7
4. 8

Correct answer: 6

Solution

Let A=sqrt(2x^2+1), B=sqrt(2x^2-1); then (A+B)(A-B)=2 so 2/(A+B)=A-B. The sum (A+B)^6+(A-B)^6 = 2(A^6+15A^4B^2+15A^2B^4+B^6), a polynomial in A^2,B^2. It simplifies to 512x^6-96x^2, which has degree 6.

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