For `x le 2," solve "x^(3)3^(|x-2|)+3^(x+1) = x^(3)*3^(x-2)+3^(|x-2|+3)`

Answer

x = 2

Explanation

Clearly , x = 2 satisfies the given equation.
For ` x lt 2`, equation becomes
` x^(3)3^(2-x)+3^(x+1) = x^(3)* 3 ^(x-2) + 3 ^(5 - x)`
` rArr 3^(2-x)(x^(3)-3^(3)) = 3^(x-2)(x^(3)-3^(3))`
`rArr (x^(3)-3^(3))(3^(2-x)-3^(x-2))=0`
` rArr x = 3 or x = 2`
` :. x = 2 ` is the only solution