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If (3+asqrt2)^100+(3+bsqrt2)^100=7+5sq...

If `(3+asqrt2)^100+(3+bsqrt2)^100=7+5sqrt2` number of pairs (a, b) for which the equation is true is, (a, b are rational numbers) (a) `1` (b) `6` (c) `0` (d) infinite

A

1

B

6

C

0

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`(3 + asqrt(2))^(100) + (3 + bsqrt(2))^(100) = 7 + 5 sqrt(2)`
`rArr (3 - a sqrt(2))^(100)+ (3 - b sqrt(2))^(100) = 7 - 5 sqrt(2)`
We observe that LHS `gt` 0 for all pairs (a, b). So, the above
equality is not ture for any pair (a, b) of ratinoal number.
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