Radical Functions?

Question

The height in metres of two boxes are 2x and the square root of (3x-2) . The combined height is 3x. Calculate the maximum height of each box.

It hard to when you need help with it... thought that was the point of this....

Answer 1

2x + sqrt(3x-2) = 3x
x = sqrt(3x-2)
x^2 - 3x + 2 = 0
(x-1)(x-2) = 0
x = 1 or x= 2
The max. height of the first box is 2(2) = 4 m
The max. height of the second box is [3(2)-2] = 4 m

Answer 2

Calculating the combined height of the two boxes yields a sum of 3x.
Expressed mathematically, 2x + Sq. rt of (3x-2) = 3x
Thus, Sq rt. of (3x -2) = x
Squaring both sides yields, 3x-2 = x^2
Solve for x
x= 1, 2
Creating the maxi um height requires a selection of the larger number in the solution set. (i.e. 2)
Substitution produces the following result:
2(2) = 4 m
sqr. rt. of 3(2) -2 = 2m

Answer 3

If one box is 2x high, and the other box is sqrt(3x-2) high, and they add to 3x, we can write:

2x + sqrt(3x-2) = 3x

Now we do some algebraic manipulation:

2x + sqrt(3x-2) = 3x
sqrt(3x-2) = x
(3x-2) = (x)^2
3x - 2 = x^2
0 = x^2 - 3x + 2

From here, use the quadratic formula, or factoring, to find that
x = 2
or
x = 1

The first of these is larger, so plug that x-value back into the original formulas for the box heights to get the answers.

Answer 4

2x + (3x - 2)^(1/2) = 3x
(3x - 2)^(1/2) = x
3x - 2 = x²
x² - 3x + 2 = 0
(x - 2).(x - 1) = 0
x = 1 , x = 2
Maximum heights are 4m and 2m.