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serg [7]
3 years ago
7

Pls help i am on a timer

Mathematics
1 answer:
stich3 [128]3 years ago
3 0

Answer:

x = 1 + \sqrt{2} \ \ or \ 1- \sqrt{2}

Step-by-step explanation:

Given;

x² - 2x - 1 = 0

Solve by completing the square method;

⇒ take the constant to the right hand side of the equation.

x² - 2x = 1

⇒ take half of coefficient of x = ¹/₂ x -2 = -1

⇒ square half of coefficient of x and add it to the both sides of the equation

x^2 +  (-1)^2 = 1 + (-1)^2

(x-1)^2 = 1 + 1\\\\(x-1)^2 = 2\\\\

⇒ take the square root of both sides;

x-1 = +/- \ \ \sqrt{2} \\\\x = 1 + \sqrt{2} \ \ or \ 1- \sqrt{2}

Therefore, option B is the right solution.

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Plane-1 = Boston, Massachusetts - Seattle, Washington at 10:00 AM

Plane-2= Seattle, Washington - Boston, Massachusetts at 11:00 AM

Speed of plane-1 = 300 mile/hour

Distance covered by plane-1 in 1 hour = 300 mile/h × 1 h = 300 mile

Distance between plane-1 and plane 2 after 1 hour :

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Let the distance covered by plane-1 after 1 hour be x in t time where it will pass plane-2.

Let the distance covered by plane-2 be y in t time where it will pass plane-1.

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300 mile/h=\frac{x}{t}..[2]

Speed of plane-2 = 300 mile/hour

300 mile/h=\frac{y}{t}..[3]

Putting value of t from [2] in [3];

t=\frac{x}{300 mile/h}

300 mile/h=\frac{y}{\frac{x}{300 mile/h}}

\frac{x}{300 mile/h}=\frac{y}{300 mile/h}

x = y

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2y = 2700 miles

y = 1,350 mile

For the value of t, put the value of y in [3]:

t=\frac{1,350 mile}{300 mile/h}=4.5 hour

The plane from Seattle will pass the plane from Boston after 4.5 hours of its departure from the Seattle.

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