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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
`(c )` `(3+asqrt(2))^(100)+(3+bsqrt(2))^(100)=7+5sqrt(2)`
since `a` and `b` are rational
`(3-asqrt(2))^(100)+(3-bsqrt(2))^(100)=7-5sqrt(2)`
Here `R.H.S. lt 0` but `L.H.S. gt 0`
So there are no such pairs `(a,b)`
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