Answer:
x = 2
Step-by-step explanation:
These equations are solved easily using a graphing calculator. The attachment shows the one solution is x=2.
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<h3>Squaring</h3>
The usual way to solve these algebraically is to isolate radicals and square the equation until the radicals go away. Then solve the resulting polynomial. Here, that results in a quadratic with two solutions. One of those is extraneous, as is often the case when this solution method is used.
The solutions to this equation are the values of x that make the factors zero: x=2 and x=-1. When we check these in the original equation, we find that x=-1 does not work. It is an extraneous solution.
x = -1: √(-1+2) +1 = √(3(-1)+3) ⇒ 1+1 = 0 . . . . not true
x = 2: √(2+2) +1 = √(3(2) +3) ⇒ 2 +1 = 3 . . . . true . . . x = 2 is the solution
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<h3>Substitution</h3>
Another way to solve this is using substitution for one of the radicals. We choose ...
Solutions to this equation are ...
u = 2, u = -1 . . . . . . the above restriction on u mean u=-1 is not a solution
The value of x is ...
x = u² -2 = 2² -2
x = 2 . . . . the solution to the equation
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<em>Additional comment</em>
Using substitution may be a little more work, as you have to solve for x in terms of the substituted variable. It still requires two squarings: one to find the value of x in terms of u, and another to eliminate the remaining radical. The advantage seems to be that the extraneous solution is made more obvious by the restriction on the value of u.
Answer:
30 cups of flour
Step-by-step explanation:
3 x 8 = 24
3/4 x 8 = 24/4 = 6
24 + 6 = 30
Answer:
Step-by-step explanation:
=> 2 gallons of milk each day.
<u>This means</u>
1 day = 2 gallon of milk
Multiply both sides by 5
5 (1 day) = 5 (2 gallons of milk)
<h3>5 days = 10 gallons of milk</h3>
Hope this helped!
<h3>~AH1807</h3>
Cost/ ounce
16 ounce $1 16 ounce
_________ × _________ = __________ ≈ 19 ¢ per ounce
$ 3.20 100 ¢ 320
<h2>
Greetings!</h2>
Answer:
$12.60
Step-by-step explanation:
To find this, you need to remember this equation:
Starting amount x
Plug these values in:
18 x = 12.6
So the clearance price was $12.60!
<h2>Hope this helps!</h2>