Please show me how to do these step by step because I have a test tomorow and I need to understand how to do these questions :
1. M-1 under the square root sign +5= m-2
2. 3n+10 under the square root = n+4
3. K-9 under the square root - (k under square root )=-1
4. 2h-5 under square root =1- ( h-3) under square root
Please explain :)
1. √(m-1) + 5 = m-2
√(m-1) = m - 7
square both sides
m-1 = m^2 - 14m + 49
m^2 - 15m + 50 = 0
(m-5)(m-10) = 0
m = 5 or m = 10
BUT, since we squared the equation, all answers MUST be verified in the original equation.
if m = 5
LS = √(5-1) + 5
= 2 + 5 = 7
RS = 5-2 = 3
LS ≠ RS
if m = 10
LS = √9 + 5 = 8
RS = 10-2 = 8
LS = RS
So m = 10 is the only solution
Use the same method for the other two equations
Oh thank u so much:) hopefully I can pass the test!
Sure! I'd be happy to help you understand how to solve these questions step by step. Let's go through each problem one by one:
1. M-1 under the square root sign + 5 = M-2
To solve this equation:
- Start by isolating the square root term on one side of the equation. In this case, subtract 5 from both sides of the equation:
M-1 under the square root sign = M-2 - 5
M-1 under the square root sign = M-7
- Now, square both sides of the equation to eliminate the square root:
(M-1 under the square root sign)^2 = (M-7)^2
M-1 = (M-7)(M-7)
M-1 = M^2 - 14M + 49
- Simplify the equation:
M-1 = M^2 - 14M + 49
- Move all terms to one side of the equation to set it to zero:
M^2 - 15M + 50 = 0
- Factor or use the quadratic formula to solve for M in this quadratic equation.
2. 3n+10 under the square root = n+4
To solve this equation:
- Begin by isolating the square root term on one side of the equation. In this case, subtract n+4 from both sides:
3n+10 under the square root = n+4 - (n+4)
3n+10 under the square root = 0
- Square both sides of the equation to eliminate the square root:
(3n+10 under the square root)^2 = 0^2
3n+10 = 0
- Solve for n:
3n = -10
n = -10/3
3. K-9 under the square root - (K under square root) = -1
To solve this equation:
- First, remove parentheses following order of operations. In this case, distribute the negative sign:
K-9 under the square root - K under the square root = -1
- Combine the two square root terms:
(K-9 - K) under the square root = -1
(-9) under the square root = -1
- Square both sides of the equation to eliminate the square root:
(-9)^2 = (-1)^2
9 = 1
No solution. Since 9 does not equal 1, there is no solution to this equation.
4. 2h-5 under the square root = 1 - (h-3) under the square root
To solve this equation:
- Begin by isolating the square root term on one side. In this case, move (h-3) under the square root to the left side by subtracting it from both sides:
2h-5 under the square root + (h-3) under the square root = 1
- Combine the two square root terms:
(2h-5 + h-3) under the square root = 1
(3h-8) under the square root = 1
- Square both sides of the equation to eliminate the square root:
(3h-8)^2 = 1^2
9h^2 - 48h + 64 = 1
- Simplify the equation:
9h^2 - 48h + 63 = 0
- Factor or use the quadratic formula to solve for h in this quadratic equation.
Remember to always double-check your answers and solution process to ensure accuracy. Good luck with your test!