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Let a, b, c, d, e, f be nonnegative real numbers.
(a) Prove that
\((a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) \ge (ace + bdf)^4.\)
(b) Prove that
\((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2.\)