Move one radical to the other side, then square, thereby yielding an equation with only one radical.

Isolate the radical on one side, then square.

替换证实这是唯一的解决方案.

The area of a rectangle is, where A is the area, L is the length, and W is the width. The perimeter is given by. We know thatand. We can solve for L usingThe perimeter is thenfeet.

Cube both sides of the equation to form a linear equation, then solve:

方程1:

Equation 2:

Equation 3:

Adding the terms of the first and second equations together will yield.

Then, add that to the third equation so that the y and z terms are eliminated. You will get.

This tells us that x = 1. Plug this x = 1 back into the systems of equations.

现在,我们可以通过使用th做其余的问题e substitution method. We'll take the third equation and use it to solve for y.

Plug this y-equation into the first equation (or second equation; it doesn't matter) to solve for z.

We can use this z value to find y

So the solution set is x = 1, y = 2, and z = –5/3.

To solve this problem we can first addto each side of the equation yielding

Then we take the square root of both sides to get

Then we calculate the square root ofwhich is.

We can solve the system of equations using the substitution method.

Solve forin the second equation.

Substitute this value ofinto the first equation.

Now we can solve for.

Solve forusing the first equation with this new value of.

The solution is the ordered pair.

By substituting- and, subsequently,这可以写成一个二次方程equation, and solved as such:

We are looking to factor the quadratic expression as, replacing the two question marks with integers with productand sum 5; these integers are.

Substitute back:

The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:

Set each factor to zero and solve:

Since no real number squared is equal to a negative number, no real solution presents itself here.

The solution set is.

Subtract 12 from both sides:

–3x = –15

Divide both sides by –3:

x = 5

Distribute the x through the parentheses:

x²–2x = x²– 8

Subtract x²from both sides:

–2x = –8

Divide both sides by –2:

x = 4

Add 5 to both sides to isolate the cube root:

Cube both sides:

To isolate, move it to the right side of the equation. We choose the right side instead of the left side so as to makepositive:

Subtract 125 from both sides to isolate: