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Algebra Level 4

Find the minimum value of \(1+{ a }^{ 4 }+{ b }^{ 8 }\) if a and b are positive real numbers with \(a{ b }^{ 2 }=5\).


You may even like a tougher and a bit more challenging question by me which is in sequel to this.
If you want to help me and others in NMTC final level problems then you may even like this.
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