Solve the equation.

Question

Solve the equation.

 

√¯¯¯¯¯        √¯¯¯¯¯¯

  3x +1 = 3 + x - 4

Answer 1

√(3x+1) = 3 + √(x-4)

 

Square both sides:

 

3x + 1 = 9 + 6√(x-4) + x - 4

 

2x - 4 = 6√(x-4)

 

x - 2 = 3√(x-4)

 

Square both sides:

 

x^2 - 4x + 4 = 9x - 36

 

x^2 - 13x + 40 = 0

 

x = (-(-13) ± √((-13)^2 - 4(1)(40)))/(2(1))

 

x = (13 ± √(169 - 160))/2

 

x = (13 ± 3)/2

 

x = 5 or 8

 

check:

 

√(3(5)+1) =? 3 + √((5)-4)

4 = 3 + 1 √

 

√(3(8)+1) =? 3 + √((8)-4)

5 = 3 + 2 √