If \( (3+a \sqrt{2})^{100}+(3+b \sqrt{2})^{100}=7+5 \sqrt{2} \), number of pairs \( (a, b) \) fo...

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If \( (3+a \sqrt{2})^{100}+(3+b \sqrt{2})^{100}=7+5 \sqrt{2} \), number of pairs \( (a, b) \) for which the equation is true is, \( (a, b \) are rational numbers)
(A) 1
(B) 6
(C) infinite
(D) undefined
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