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Delta(1)=|{:(x,b,b),(a,x,b),(a,a,x):}| a...

`Delta_(1)=|{:(x,b,b),(a,x,b),(a,a,x):}|` and `Delta_(2)=|{:(x,b),(a,x):}|` are the given determinations then

A

`Delta_(1)=3(Delta_(2))^(2)`

B

`(d)/(dx)(Delta_(1))=3Delta_(2)`

C

`(d)/(dx)(Delta_(1))=3(Delta_(2))^(2)`

D

`Delta_(1)=3Delta_(2)^(3//2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `Delta_(1)=x(x^(2)-ab)-b(ax-ab)+b(a^(2)-ax)`
`=x^(3)-3abx+ab^(2)+a^(2)b`
`:.(d)/(dx)(Delta_(1))=3x^(2)-3ab=3(x^(2)-ab)=3Delta_(2)`
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