To solve the equation √(2x) + 5 = 1 using mental math, we can follow these steps:
Subtract 5 from both sides of the equation: √(2x) = -4
Square both sides of the equation to eliminate the square root: 2x = 16
Divide both sides by 2 to solve for x: x = 8
Therefore, the solution to the equation √(2x) + 5 = 1 is x = 8.
Regarding the problem m +4-√3m = 0, we can solve for m algebraically by following these steps:
Move the constant term (4) to the other side of the equation: √(3m) = -m + 4
Square both sides to eliminate the square root: 3m = (4 - m)^2
Simplify the right-hand side: 3m = 16 - 8m + m^2
Rearrange the terms and set equal to zero: m^2 - 11m + 16 = 0
Factor the quadratic equation: (m - 1)(m - 16) = 0
Solve for m by setting each factor equal to zero: m - 1 = 0 or m - 16 = 0
Solve for m in each equation: m = 1 or m = 16
Therefore, the solutions to the equation m +4-√3m = 0 are m = 1 and m = 16.