Solution of the equation `3^(2x^2)-2.3^(x^2+x+6)+3^(2(x+6))` =0 is

Options

A. `{-3,2}`
B. `{6,-1}`
C. `{-2,3}`
D. `{1,-6}`

Answer

C

Explanation

We have `3^(2x^(2))-2.3^(x^(2)+x+6)+3^(2(x+6))=0`
`implies(3^(x^(2))-3^(x+6)^(2)=0`
`implies3^(x^(2))-3x^(x+6)=0`
`implies3^(x^(2))-3^(x+6)=0`
`=3^(x^(2))=3^(x+6)impliesx^(2)-x+6`
`impliesx^(2)-x-6=0`
`implies(x-3)(x+2)=0`
`:.x={-2,3}`