To solve the equation √n/4 = √(5-n), we can start by squaring both sides of the equation:
(√n/4)^2 = (√(5-n))^2
Canceling out the square roots gives us:
(n/4)^2 = (5-n)
Expanding both sides of the equation further, we have:
n^2/16 = 25 - 10n + n^2
Now, let's simplify the equation by multiplying both sides by 16 to eliminate the fraction:
n^2 = 400 - 160n + 16n^2
Rearranging the equation by combining like terms:
15n^2 + 160n - 400 = 0
To simplify this quadratic equation, we can divide through by 5:
3n^2 + 32n - 80 = 0
Now, we can try to factorize the equation:
(3n - 8)(n + 10) = 0
Setting each factor equal to zero gives us two possible solutions:
3n - 8 = 0
n + 10 = 0
Solving for n in each case:
3n = 8
n = 8/3
n = -10
Therefore, the possible solutions for n are n = 8/3 and n = -10.
I HOPE THIS HELPS.
okay so question 2
To solve the equation √m - 4 = √10-m, we can start by isolating one of the square roots on one side of the equation.
Let's begin by moving the square root term involving m to one side:
√m - √10 + m = 4
Next, let's square both sides of the equation to eliminate the remaining square roots:
(√m - √10 + m)^2 = 4^2
Expanding the squared term gives us:
(m - 2√(10)m + 10 - 4√m + 2m√(10) + m^2) = 16
Rearranging the equation and simplifying like terms:
m^2 + 3m√(10) - 4√m - 2√(10)m - 14 = 0
Factoring out common factors:
(m^2 + m(3√10 - 2√10) - 4√m - 14 = 0
Simplifying further:
(m^2 + m√10 - 4√m - 14) = 0
Now, at this point, it is difficult to directly factor or simplify the equation further. One way to proceed is to use numerical methods or solvers to find an approximate value for m that satisfies the equation. Alternatively, graphical methods can also be used to find a solution.