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Algebra Difficulty 1.6 Junior Find the answer

When simplified 1+(x4−12x2)2\sqrt{1+ \left (\frac{x^4-1}{2x^2} \right )^2} equals:

Pick one

Solution

4x44x4+(x4−1)24x4  ⟹  x8−2x4+1+4x44x4  ⟹  (x4+1)2(2x2)2  ⟹  x4+12x2  ⟹  x22+12x2\sqrt{\frac{4x^4}{4x^4}+\frac{(x^4-1)^2}{4x^4}}\implies\sqrt{\frac{x^8-2x^4+1+4x^4}{4x^4}}\implies \sqrt{\frac{(x^4+1)^2}{(2x^2)^2}}\implies \frac{x^4+1}{2x^2}\implies\frac{x^2}{2}+\frac{1}{2x^2}, E\fbox{E}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.