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
konstantin123 [22]
3 years ago
14

2.√3x + 7 + √x + 1 =2​

Mathematics
1 answer:
taurus [48]3 years ago
5 0

Answer:

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

  \displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

You might be interested in
Samantha works at a nursery where she pots plants. It takes her 1 1/2 hours to pot 12 plants. How many plants can Samantha pot i
ahrayia [7]
She can plot 9 in 1 hour
3 0
3 years ago
Today, everything at a store is on sale. The store offers a 20% discount. The regular price of a shirt is $14. What is the disco
USPshnik [31]

Answer:

$11.20

Step-by-step explanation:

The regular price of the T-Shirt is $14 dollars. The discount is 20% off.

20 percent of 14:

14 * 0.2 = 2.80

You would save $2.80.

14 - 2.80 = 11.20

The discount price should be $11.20.

Hope this helps.

4 0
3 years ago
A painting is 16 in wide and 8 in tall if it is reduced to a height of 2 in then how wide will it be
allochka39001 [22]

Answer: 4 in. wide

Step-by-step explanation: to get from 8 to 2, you divide by 4.

if you divide 16 by 4, the answer is 4

7 0
3 years ago
Read 2 more answers
What function type does the table of values represent? Question 7 options: A) Linear B) Quadratic C) Exponential D)
DanielleElmas [232]
Linear because there is a constant change (+3)
4 0
2 years ago
Someone plzzz solve this for meee will mark brainiestttt
Roman55 [17]

Answer:

1. rational number

3. subset

4. repeating decimals

5. additive inverse

6. terminating decimals

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Michael threw for 1,654 yards in his first five games. At this rate, how many yards will he have thrown for in fifteen games? ✗
    6·2 answers
  • Can someone show me how to find the product of 3square-root(4) * square-root(3)?
    15·1 answer
  • What is sum of all odd numbers between 100 and 200
    7·1 answer
  • You are in charge of buying food for your family reunion. You spent $90 on hamburgers and turkey burgers. you pay $1.50 for each
    11·1 answer
  • Would C(m)=6x+25 domain be best represented by integers whole numbers rational numbers or real numbers
    10·1 answer
  • 3. A tunnel is 300 feet deep and makes an angle of 30° with the ground, as shown below.
    6·1 answer
  • Does anyone know how to do this ??? <br> -view attachment
    11·1 answer
  • Please help me with this
    15·2 answers
  • 1 Mrs. Castro has 100 spoon and 80 forks if she put them in buckets what is the biggest number of spoon or forks that bucket wil
    11·1 answer
  • Are you subscribed to technoblade? serious question.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!