Solve the equation x^2 -6x -23 =0. Simplify ALL IRRATIONAL SOLUTIONS. Select from the following:
a) x={4 plus or minus 3 square root 2 2/3
b) x = { 3 plus or minus 4 square root 2 2/3
c) x = { plus or minus square root 32 2/3
d) x = {-3 plus or minus 4 square root 2 2/3
To solve the quadratic equation x^2 - 6x - 23 = 0, we can use the quadratic formula:
x = [-(-6) ± √((-6)^2 - 4(1)(-23))] / 2(1)
x = [6 ± √(36 + 92)] / 2
x = [6 ± √128] / 2
x = [6 ± 8√2] / 2
x = 3 ± 4√2
Therefore, the solutions are x = 3 + 4√2 and x = 3 - 4√2.
So the irrational solutions are:
- x = {3 + 4√2, 3 - 4√2}
The correct choice is:
b) x = { 3 plus or minus 4 square root 2 2/3