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If a,ba,ba,b are the roots of x2+ωx−12ω2=0x^{2}+\omega x-\frac{1}{2\omega ^{2}}=0x2+ωx−2ω21=0, where ω\omega ω is a positive constant, find the minimum value of a4+b4a^{4}+b^{4}a4+b4.
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