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]
2 years ago
13

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

Mathematics
1 answer:
Semenov [28]2 years 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
What is the slope of the line that passes through the points (1,0) and (5, 3)?
Varvara68 [4.7K]

Answer:

Undefined

Step-by-step explanation:

6 0
3 years ago
What are the answers
gulaghasi [49]

Answer and Step-by-step explanation:

7. 70 - 180 = 110

8.  39 - 180 = 141

9. 81 - 180 = 99

10. 81 - 180 = 99

11. 115 - 180 = 65

12.  41+36 = 77 - 180 = 103

x = answer

4 0
3 years ago
How do you solve this by grouping x^3-3x^2+3x-9=0
frozen [14]

Answer:

x = 3

x = ± √3 = ± 1.7321

6 0
3 years ago
Read 2 more answers
Tickets for the basketball game cost 14$ each. If the sale of the tickets brought in 2,212$, how many tickets were sold?
rosijanka [135]
15.78 is the answer to the qustion that you have asked.
5 0
3 years ago
What is 7.06 divide 0.353
solong [7]
7.06 ➗ 0.353= 20

Hope this helps! :3
3 0
3 years ago
Other questions:
  • (y^4)^4 what would that answer be please gibe a real anwer this time please
    10·2 answers
  • Help me pls I'm stuck......
    12·1 answer
  • NASA is painting the nose cone of a sounding rocket with a special sealant which reduces the air-drag on the rocket. If they nee
    13·1 answer
  • What is y=21 times 8×34
    14·1 answer
  • I NEED HELP WITH C. SOMEONE PLEASE
    5·1 answer
  • (3x + 8)
    14·1 answer
  • 100 points on the line
    7·2 answers
  • Yessica earns $15/hour and Claire earns $12/hour. If Yessica worked x hours and Claire worked 20 hours find the total amount of
    7·1 answer
  • Sandra saves 10% of her salary for retirement. This year her salary was $2,000 more than in the previous year, and she saved $4,
    8·2 answers
  • Given that Cos0=5/13,find a)Tan0,b)Sin0,c)Sec0,d)Co sec0,e)Cot0,​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!