Could someone help me out with this plss

The value of

marusya05 [52]

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

We have to find out the value of the fraction.

Let us assume that:

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

We can also write it as:

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

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

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

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

Comparing the given equation with ax² + bx + c = 0, we get:

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

By quadratic formula:

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

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

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

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

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

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

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

But "x" cannot be negative. Therefore:

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

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

4 0

2 years ago

The diagram shows squares 1 2 and 3

nikklg [1K]

(Area of 1) + (Area of 2) = (Area of 3) this statement about the squares must be true.

What is Right angle traingle?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. The triangle's base and perpendicular sides both include the right angle. The longest of the three sides, known as the hypotenuse, is the third side.

we know that;

By applying the Pythagorean Theorem;

$c^2 = a^2 + b^2$ .............................(1)

Area of the square says A1;

A1 = a^2 unit^2 ...............................(2)

Area of the square says A2;

A2 = b^2 unit^2 .................................(3)

Area of the square says A1;

A3 = c^2 unit^2 ..................................(4)

Replace the A1, A2, and A3 values in the equation 1 ;

A3 = A1 + A2

therefore;

(Area of 1) + (Area of 2) = (Area of 3).

Learn more about right angled triangle click here:

brainly.com/question/22790996

#SPJ4

8 0

9 months ago

The system of equations Y =-3x+2 and Y = 3x-6 is shown on the graph below.

Ira Lisetskai [31]

Answer:

A

Step-by-step explanation:

8 0

3 years ago

Linear equations assignment:

Daniel [21]

Answer:

20 laps

Step-by-step explanation:

2 times = +1 dollars for Paula, +0.50 dollars for Jacki

Try multiplying it the least amount of times to Paula can have more and so 20 times and Paula will have 20 dollar sand Jacki will have 19.75, therefore she needs to do 20 laps.

6 0

2 years ago

If 900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible v

pentagon [3]

Answer:

1400

Step-by-step explanation:

6 0

2 years ago