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
pogonyaev
3 years ago
15

Is the solution of this equation extraneous?

Mathematics
2 answers:
UkoKoshka [18]3 years ago
6 0

Answer:

x = - 3 is extraneous

Step-by-step explanation:

Given

\sqrt{x+7} - 1 = x  ( add 1 to both sides )

\sqrt{x+7} = x + 1 ( square both sides )

x + 7 = (x + 1)² ← distribute right side

x + 7 = x² + 2x + 1 ( subtract x + 7 from both sides )

0 = x² + x - 6 ← in standard form

0 = (x + 3)(x - 2) ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = - 3 : \sqrt{-3+7} - 1 = \sqrt{4} - 1 = 2 - 1 = 1 ≠ - 3

x = 2 : \sqrt{2+7} - 1  = \sqrt{9} - 1 = 3 - 1 = 2

x = 2 is a solution and x = - 3 is extraneous

Katarina [22]3 years ago
6 0

Good morning ☕️

____________________

Step-by-step explanation:

Look at the photo below for the answer.

:)

You might be interested in
What is the prime factorization of 72?
yawa3891 [41]
Prime factorization can be obtained by the factor tree
72=2*36=2*(2*18)=2*(2*(2*9))=2*2*2*3*3=2^3*3^2
8 0
3 years ago
Read 2 more answers
Write the slope-interest form of the equation that passes through (-2,6) with a slope of 3/2
iVinArrow [24]

Answer:

y = 3/2x+6

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Porfa ayudenme con este ejercicio.
Daniel [21]
D) La camisa roja y el pantalon negro
4 0
3 years ago
Read 2 more answers
Please need help on this one
tekilochka [14]
On which one do you need help with?
4 0
3 years ago
At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The num
const2013 [10]

Answer:

B

Step-by-step explanation:

The given equations satisfy the given conditions. There are 2 equations and 2 unknowns, so a certain solution can be found.

This can be solved using substitution,

Substituting eqn 2 to eqn 1:

2(2y – 10) + 3y =1240

Simplifying,

y = 180

x = 350

5 0
3 years ago
Other questions:
  • Sam bought brushes for 8$ a palette for 5$ and oil paints for 15$ he paid 29.82 in all what sales tax rate did sam pay
    14·1 answer
  • Martina is practicing her free-throw shots. So far, she has made 16 out of 20 shots. If she attempts 80 more shots and shoot wit
    12·1 answer
  • 3/16=(-5/4)+g please help me
    14·1 answer
  • Four houses require 1,800 square feet, 1,050 square, 1,200 squares feet, and 1,460 square feet of shingles, respectively, How ma
    7·1 answer
  • Need answer ASAP! Thanks in advance!
    11·2 answers
  • Circle two ascends to add first. Find the sum. Explain your strategy. 7+3+2
    6·1 answer
  • Hey i need help ASAP!
    15·2 answers
  • What is an equation of the line that is perpendicular to 2x + y = -4 and passes through the point (2, -8)?
    13·1 answer
  • Help . Describe the graph of a function g by observing the graph of the base function f.
    5·1 answer
  • What is the answer for 7 + -3​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!