Solve the equation x squareroot 3x 2 4 Find f12 given tha

Solve the equation. x - squareroot 3x - 2 = 4 Find f[1/2] given that f(x) = 4x^3 - 4x^2 - 7x; find f[1/2]

x- sqrt(3x-2)=4

sqrt(3x-2)= x-4

squaring both sides

3x-2=(x-4)²= x²-8x +16

x²-11x+18=0

(x-2)(x-9)=0

x=2,9

Checking the solutions

x-sqrt(3x-2)

2-sqrt(3(2)-2) = 2-2=0 But the right side is 4. Hence x=2 is not the solution

9-sqrt(3(9)-2) = 9 -5=4 that is the right side

Hence the solution is x=9

4. f(x)= 4x³-4x²-7x

f(1/2)= 4(1/2)³-4(1/2)²-7(1/2) = 1/2 -1 -7/2 = -4