part A solve the equation and.show all nesscary steps sqrt2x+10-1=X
Part b which solution is extraneous
Part A:
Given equation: √(2x + 10) - 1 = x
Step 1: Add 1 to both sides of the equation
√(2x + 10) = x + 1
Step 2: Square both sides to get rid of the square root
(√(2x + 10))^2 = (x + 1)^2
2x + 10 = x^2 + 2x + 1
Step 3: Rearrange the terms to set the equation equal to zero
0 = x^2 + 1 - 10
0 = x^2 - 9
Step 4: Factor the equation
0 = (x - 3)(x + 3)
Step 5: Set each factor equal to zero and solve for x
x - 3 = 0
x = 3
x + 3 = 0
x = -3
Therefore, the solutions to the equation are x = 3 and x = -3.
Part B:
To determine which solution is extraneous, we need to check each solution back into the original equation √(2x + 10) - 1 = x.
1. For x = 3:
√(2(3) + 10) - 1 = 3
√(16) - 1 = 3
4 - 1 = 3
3 = 3
2. For x = -3:
√(2(-3) + 10) - 1 = -3
√(4) - 1 = -3
2 - 1 = -3
1 = -3
Since the solution x = -3 leads to a false statement, it is the extraneous solution. The correct solution is x = 3.