1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kow [346]
3 years ago
9

Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Us

e the equation below as a model.
a√x+b+c=d

Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.

Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.

Part 3. Explain why the first equation has an extraneous solution and the second does not.
Mathematics
2 answers:
love history [14]3 years ago
8 0

Answer:

1)a) \sqrt{2x+3}=x b)\sqrt{x+5}=3 2) Solving and Checking on section 1 3) Commonly when we square both sides and there's an x on the right side outside the radical equation, an extraneous solution arises.

Step-by-step explanation:

1 &2) An extraneous solution does not satisfy an equation. So let's evaluate:

a=1,b=3,c=0, d=x}

\sqrt{2x+3}=x

\sqrt{2x+3}=x\\\left ( \sqrt{2x+3} \right )^{2}=\left (x\right)^{2}\\2x+3=x^{2}\\-x^{2}+2x+3=0\:*(-1)\\x^{2}-2x-3=0\\(x-3)(x+1)=0\\x'=-1, x''=3 \\S=\left \{ -1,3 \right \}

Checking for extraneous solution:

\sqrt{2(-1)+3}=-1\\\sqrt{3-2}=-1\\\sqrt{1}\neq-1\\1\neq -1\\\therefore -1 \:is \:an\:extraneous\:solution

\sqrt{2(3)+3}=3\\\sqrt{6+3}=3\\\sqrt{9}=3\\3= 3\\\therefore 3 \:satisfies\:the\:equation.

1 and 2) Another radical equation:

a=1, b=5,c=0, d=3

\sqrt{x+5}=3\\\left ( \sqrt{x+5}\right )^{2}=3^{2}\\x+5=9\\x=9-5\\x=4\\S=\left \{ 4\right \}

Checking:

\sqrt{x+5}=3\\\left ( \sqrt{4+5} \right )^{2}=3^{2}\\4+5=9\\9=9\\

4 satisfies the equation.

3) Because when we change the radical equation into quadratic one, and both sides are squared, very often the second solution does not satisfy the equation. That happened when we squared x.

Airida [17]3 years ago
6 0
A+x=bxc
bc=aa 
bc=a
esa es la respuesta final
You might be interested in
A rectangle is 12cm long and 9cm wide . calculate the length of the diagonal​
Shalnov [3]

Answer: 15 centimeters

Step-by-step explanation: You cut the rectangle into two triangles following the diagonal. You add 12 squared (144) and 9 squared (81) together. You get 225. You get the square root of 225 which is 15 and that is your answer. Basic solving for the hypotenuse.

4 0
2 years ago
Read 2 more answers
Identify the number that does not belong with the other three. Explain your reasoning. 50.1 repeating 1, negative 50 over 2, neg
Reika [66]
Square root 50 does not belong....all of the other numbers are rational numbers. square root 50 is irrational.
4 0
3 years ago
The jogger can run at an average speed of 5.5 miles per hour up the slope and 6.5 miles per hour going down the slope. The jogge
Bond [772]
<span>DOC]<span>Venn Diagram Task – Differentiation - Summer Summit

paste that into google and the last page is the answer sheet</span></span>
7 0
2 years ago
The perimeter of a rectangle is 42 feet the length is 5 feet longer than the width what are the dimensions
Kruka [31]
18.5 x 23.5 is the answer
7 0
3 years ago
Hakim deposited $50 in a saving account earning 10% interest, compounded annually . To the nearest cent , how much interest will
Paraphin [41]

\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}

\bf A=50\left(1+\frac{0.10}{1}\right)^{1\cdot 2}\implies A=50(1.1)^2\implies A=60.5 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{earned interest}}{60.5 - 50\implies 10.5}~\hfill

7 0
3 years ago
Read 2 more answers
Other questions:
  • Multiply (6 -7i)(3 - 6i)
    9·1 answer
  • What will always exist in any economic system?
    15·2 answers
  • The Circumference of a circle is 12 Units. What is the area?
    9·2 answers
  • Stan's Dteakhous3 has a server to cook ratio pf 5 to 2. The total number pf servers and cooks is 42. How many servere does Stan'
    5·1 answer
  • How to write three hundred thousand, five thousand sixty three in standard form
    9·2 answers
  • one number is equal to the square of another. find the numbers if both are positive and their sum is 1122
    7·1 answer
  • What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?
    13·1 answer
  • A boat is carrying containers that weigh 4000 pounds each.
    9·1 answer
  • CAN SOMEONE HELP ME PLEASE ASAP!?
    5·2 answers
  • Mohamed plants 30 roses in 5 plots,if he needs to plant 120 roses,how many plots he needs ?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!