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
Tamiku [17]
3 years ago
10

What reasoning and explanations can be used when solving radical equations and how do extraneous solutions arise from radical eq

uations?
Mathematics
1 answer:
Mkey [24]3 years ago
7 0

Answer:

We know that, a 'radical equation' is an equation that contains radical expressions, which further are the expressions containing radicals ( square roots and other roots of numbers ).

In order to solve radical equations, we use the rules of exponents and basic algebraic properties.

The common reasoning to use while solving a radical equation is:

1. Isolate the radical expression.

2. Square both sides of the equation to remove radical.

3. After removing the radical, solve the equation to find the unkown variable

4. Check the answer for the errors occurred by removing the radicals.

For e.g. \sqrt{x}-3=5

i.e. \sqrt{x}-3+3=5+3 ( Adding 3 on both sides )

i.e. \sqrt{x}=8

i.e. (\sqrt{x})^{2} =8^{2}

i.e. x=64.

So, the solution the the radical equation \sqrt{x}-3=5 is x = 64.

Further, we know that an 'extraneous solution' is that root of the radical equation which is not a root of the original equation and is excluded from the domain.

for e.g. Take \sqrt{x+4} =x-2

i.e. (\sqrt{x+4})^{2} =(x-2)^2

i.e. x+4=x^2+4-4x

i.e. 0=x^2-5x

i.e. 0=x(x-5)

i.e. x = 0 and x = 5.

Substituting x = 0 in \sqrt{x+4} =x-2, gives \sqrt{0+4} =0-2 i.e. \sqrt{4} =-2 i.e. 2=-2, which is not possible.

So, x = 0 is a solution that does not satisfy the equation.

Hence, x = 0 is an extraneous solution.

You might be interested in
A bag contains 4 red and 6 green gumballs. if you select 5 of them without looking, how many ways can you get exactly 3 red or e
marusya05 [52]
This is a combination problem. The approach to this is by using the nCr method, where n is the number of total objects and r is the number of success. For example, if you want to get 3 red out of the total 4, then that would be 4C3. That means,

4C3 = 4!/3!(4 - 3)! = 4 ways

If you want to get 2 green out of the total 6, then that would be 6C2. That means,

6C2 = 6!/2!(6-2)! = 15 ways

Therefore, there are a total of 4+15 = <em>19 ways</em>.
8 0
3 years ago
PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was
dimulka [17.4K]

Answer:

$46.272

Step-by-step explanation:

6 0
2 years ago
Which could be the side length of a 30°-60°-90° triangle?
pshichka [43]
I believe the answer is C
5 0
3 years ago
What is the value of f(−1) when f(x)=2x+2 ?<br><br><br> Enter your answer in the box.<br> f(−1)=
lutik1710 [3]
F(-1)=2(-1)+2
f(-1)=-2+2
f(-1)=0
5 0
3 years ago
Read 2 more answers
What is the slope of the line that passes through the pair of points?
Nostrana [21]

Answer:

slope(m)=(-33/2)

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Find the X intercept show work
    10·1 answer
  • Regular hexagon ABCDEF is inscribed in a circle with center H. What is the image of segment BC after 120 degree clockwise rotati
    10·1 answer
  • Which should be filed immediately before 32754? A) 32768 B) 32636 C) 31070 D) 3275 E) 32658
    10·2 answers
  • How many monkeys were there
    11·1 answer
  • Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur
    13·1 answer
  • -0.75 7/8 and - 5/8 in order from least to greatest
    11·1 answer
  • Sara is cutting bows out of ribbon which
    9·2 answers
  • The area of a rectangular glass slab is 80 square centimeters and its perimeter is 36 centimeters. If the length and width of th
    13·1 answer
  • Can someone help me please!! :C
    9·1 answer
  • Find the value of <br>tan 45º . tan- 30° tan 60°​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!