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
Elza [17]
2 years ago
6

The value of

Mathematics
1 answer:
marusya05 [52]2 years ago
4 0

\large\underline{\sf{Solution-}}

We have to find out the value of the fraction.

<u>Let us assume that:</u>

\sf \longmapsto x =2 +   \dfrac{1}{2 +  \dfrac{1}{2 +  \dfrac{1}{2 + ... \infty} } }

<u>We can also write it as:</u>

\sf \longmapsto x =2 + \dfrac{1}{x}

\sf \longmapsto x =\dfrac{2x + 1}{x}

\sf \longmapsto  {x}^{2}  =2x + 1

\sf \longmapsto {x}^{2}  - 2x - 1 = 0

<u>Comparing </u>the given <u>equation</u> with <u>ax² + bx + c = 0,</u> we get:

\sf \longmapsto\begin{cases} \sf a =1 \\ \sf b =  - 2 \\ \sf c =  - 1 \end{cases}

<u>By quadratic formula:</u>

\sf \longmapsto x =  \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{ {( - 2)}^{2} - 4(1)( - 1)} }{2 \times 1}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{4 + 4} }{2 \times 1}

\sf \longmapsto x =  \dfrac{2 \pm \sqrt{8} }{2}

\sf \longmapsto x =  \dfrac{2 \pm2 \sqrt{2} }{2}

\sf \longmapsto x = 1 \pm\sqrt{2}

\sf \longmapsto x = \begin{cases} \sf 1  + \sqrt{2} \\ \sf 1 -  \sqrt{2}  \end{cases}

<u>But </u><u>"</u><u>x"</u><u> cannot be negative. Therefore:</u>

\sf :\implies x = 1 + \sqrt{2}

So, the value of the fraction is 1 + √2.

You might be interested in
What figure has properties of all sides congruent and all right angles?
andre [41]
A. Rectangle


Here bestie
7 0
2 years ago
What is 10.417 rounded to the nearest hundredth?
Zarrin [17]
10.417 rounded to the nearest hundredth is 10.42

Hope it helps!

7 0
3 years ago
Find the shaded area in the figure below. Then, explain the steps you used to find the area
Korolek [52]

Answer:

650.

Step-by-step explanation:

ok so first multiply the Length and the width of the rectangle together to get its area, which is 500.

to find the area of the triangle, just multiple the length times the width (15 x 20) and divide it by two. You should get 150.

Add 150 and 500 together, and that's your total area:

650.

Have a nice day dude

4 0
3 years ago
Parallelogram abcd is divided into two triangles along diagonal ac. if you know the area of the parallelogram, how do you find t
Lera25 [3.4K]

Answer :-      Just try area/2 or half the area of the triangle

6 0
3 years ago
Read 2 more answers
2. Which words could be represented by
MakcuM [25]

Answer:

Step-by-step explanation:

nobody answered yet, its between G and H, im leaning more towards G, but J and F are definitely not the answers.

I hope this helps a little bit

7 0
3 years ago
Other questions:
  • Write an algebraic rule to describe the translation C'(5, -4) -&gt; C'(-2, 1)
    12·1 answer
  • PLEASE HELP WILL REWARD BRAINLIEST
    14·1 answer
  • How would you write the following expression as a single term? 3[2 ln(x-1) - lnx] + ln (x+1)
    8·1 answer
  • Which function is equivalent to h(x) = 10x?+ 9x - 1?
    7·1 answer
  • Prove that : ⬆️⬆️⬆️<br><br>Anyone please solve that question.​
    13·1 answer
  • In a drawer there are 10 white, 8 black, and
    10·2 answers
  • What is the conjugate of 1 + √5
    15·1 answer
  • Pls answer show work, At a store, notebooks are on sale for 78% off the regular price. The cost of a notebook is represented by
    6·1 answer
  • SOMEONE SMART PLEASE HELP!! use the Pythagorean theorem to find x​
    12·2 answers
  • From a hot-air balloon, Guadalupe measures a 31^{\circ} ∘ angle of depression to a landmark that’s 316 feet away, measuring hori
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!