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If |(x, x+y, x+y+z),(2x+3x+2y, 4x+3y+2z)...

If `|(x, x+y, x+y+z),(2x+3x+2y, 4x+3y+2z),(3x+6x+3y, 10x+6y+3z)|=64` then the real value of x is

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The correct Answer is:
4
`Delta= x |{:(1,,x+y,,x+y+z),(2,,3x+2y,,4x+3y+2z),(3,,6x+3y,,10x+6y+3z):}|`
`=x^(2) |{:(1,,1,,x+y),(2,,3,,4x+3y),(3,,6,,10x+6y):}|[C_(3) to C_(3)-zC_(1),C_(2)to C_(2)-yC_(1)]`
`=x^(3) |{:(1,,1,,1),(2,,3,,4),(3,,6,,10):}|[C_(3) to C_(3)-yC_(2)]`
`=x^(3) (6-8+3) =64`
`x^(3) 64" or " x=4`
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