Solve the equation `3 ^(x+1)C_(2)+ ^(2)P_(2)x=4^(x)P_(2),x in N`.

Answer

`x=3`

Explanation

We have, `3^(x+1)C_(2)+P_(2)*x=4^(x)A_(2)`
`hArr(3(x+1)x)/(1*2)+2!x=4*x(x-1)`
`hArr3x^(2)+3x+4x=8x^(2)-8x`
`hArr5x^(2)_15x=0`
`hArr 5x(x-3)=0`
`thereforexne0` `[because x in N]`
Hence, x=3 is the solution of the given equation.