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Question: If \((2 + a\sqrt{3})^{50} + (2 + b\sqrt{3})^{50} = 5 + 4\sqrt{2}\), then number of pairs (a, b) for ...

If (2+a3)50+(2+b3)50=5+42(2 + a\sqrt{3})^{50} + (2 + b\sqrt{3})^{50} = 5 + 4\sqrt{2}, then number of pairs (a, b) for which the equation is true (a, b are rational numbers)

A

1

B

2

C

0

D

None

Answer

0

Explanation

Solution

Q (2+a3)50(2 + a\sqrt{3})^{50}+ (2+b3)50(2 + b\sqrt{3})^{50}= 5 + 42\sqrt{2}

Ž (2−a3)50(2 - a\sqrt{3})^{50}+ (2−b3)50(2 - b\sqrt{3})^{50}= 5 – 42\sqrt{2}< 0

But L.H.S. > 0

\ there is no pair (a,b)