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
7nadin3 [17]
1 year ago
13

Solve √x-1= x-3. Check for extraneous solutions.

Mathematics
1 answer:
Semenov [28]1 year ago
5 0

Step-by-step explanation:

so, "- 1" is also part of the square root ?

sqrt(x - 1) = x - 3

it is clear that for any value x < 1 we have no solution in R (as this makes the argument of the square root negative, and there is so real number solution for the square root of negative numbers).

now square the whole equation.

x - 1 = (x - 3)² = x² - 6x + 9

x² - 7x + 10 = 0

the general solution for quadratic equations is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -7

c = 10

x = (7 ± sqrt(49 - 4×1×10))/(2×1) =

= (7 ± sqrt(49 - 40))/2 = (7 ± sqrt(9))/2

x1 = (7 + 3)/2 = 10/2 = 5

x2 = (7 - 3)/2 = 4/2 = 2

x2 is probably (given the answer options) not a valid solution for the original problem, as it represents the negative solution of sqrt(x - 1).

sqrt(2 - 1) = 2 - 3

± 1 = -1

remember, every square root has always 2 solutions : a positive and a negative one.

your teacher clearly only wanted the positive solution, which is x1 = 5.

so, yes,

C. x = 5

is the correct answer.

but please send your teacher my regards and comments. he/she has to state that only the positive solution to the square root is required/allowed.

because, formally, also x = 2 is a valid solution.

and therefore, C. AND D. are correct answers !!!!

You might be interested in
There are 276 students.
Lynna [10]

Step-by-step explanation:

Number of males is

  • 276 - 158 = 118

Number of males not enrolled

  • 118 - 82 = 36

Number of females not enrolled

  • 158 - 102 = 56

(a)

The table based on data is

<u>                 Enrolled        Not enrolled      Total  </u>

<u>Male            82                  36                     118    </u>

<u>Female        102                56                     158   </u>

Total            184                 92                     276

(b)

Percentage of students were males that went to magic college

  • enrolled male / total students =           (use table above)
  • 82/276*100% = 29.71% (rounded)

(c)

Percentage of females went to magic college

  • enrolled female / total female =           (use table above)
  • 102/158*100% = 64.56% (rounded)
7 0
2 years ago
Complete the function table to find the function values of {-1, 7} for f(n) = 2n - 1.
allochka39001 [22]

Answer:

In its broadest definition, “civic education” means all the processes that ... That makes the question of good citizenship relative to the ... These questions are rarely treated together as part of comprehensive theories of civic education; ... of virtue, so would the polis itself become more virtuous and excellent.

Step-by-step explanation:

3 0
3 years ago
I need some help with this one
Mrac [35]

Answer:

300+90+9

-45=0+40+5

Step-by-step explanation:

399-45=354

8 0
2 years ago
Read 2 more answers
Idk. just say random multiples of 24.
vova2212 [387]

Answer:

Which unit rate is equivalent to 14 miles per gallon? (1 point

Step-by-step explanation:

i am so glad to hear you are Incredible in messages and please contact us at the free points and see what hi rjha is the most important to you to you amanpreet your support for your support for your child to be a child of your

6 0
3 years ago
Read 2 more answers
What is -5/8 times 2/3 equal in fraction form
anastassius [24]

Answer: -5/12

Step-by-step explanation: Before multiplying two fractions together by multiplying across their numerators and multiplying across their denominators, you should always try to cross-cancel as your first step.

So in this problem, the 2 and 8 cross-cancel to 1 and 4.

Also, watch out for your signs. In this problem we have a negative times a positive so we know that our answer will be negative.

Now we can multiply across the numerators and across the denominators.

So we have 5 · 1 which is 5 and 4 · 3 which is 12.

So our answer is -5/12.

Be very careful with your signs!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Lena is making two dishes for an event. Each batch of her mac-n-cheese recipe calls for 6 ounces of cheese and 2 tablespoons of
    7·1 answer
  • Find the digit that 3, 71 _ divisible by 9?
    12·2 answers
  • What is the value of p +9 when p=13.
    12·1 answer
  • 13. In engineering notation, the number<br> 0.000452 is expressed as
    10·1 answer
  • The number of students who participated in sports
    10·1 answer
  • PLEASE HELP!! WILL GIVE BRAINLIEST!
    8·1 answer
  • Iodine-131 is used medically to study the activity of the thyroid gland. Iodine – 131 has a half-life of about 8 days. This mean
    5·1 answer
  • Help me with these math problems
    15·1 answer
  • The top of a mountain at its highest point is 13, 385 feet above sea level. Give this height in miles to the nearest
    8·1 answer
  • 3 qt = ___ gal (it will be a decimal)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!