x(1), x(2), x(3) are three real numbers ...

`x_(1), x_(2), x_(3)` are three real numbers satisfying the system of equations
`x_(1)+3x_(2)+9x_(3)=27, x_(1)+5x_(2)+25x_(3)=125` and `x_(1)+7x_(2)+49x_(3)=343`, then which of the following options are correct

A

number of divisor of `x_(1)+x_(3)` is 6

B

`(x_(1)+x_(2))/2` is a prime number

C

`x_(3)-x_(2)` is a prme number

D

`x_(1)+x_(2)+x_(3)` is square of an integer

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The correct Answer is:

A, B, D

Roots of the equation `y^(3)-x_(3)y^(2)-x_(2)y-x_(1)=0` are 3, 5, and 7
`x_(3)=15, x_(3)=-71, x_(1)=105`

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