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Ede4ka [16]
2 years ago
6

Prove that √p is an irrational number , if p is not a perfect square.​

Mathematics
1 answer:
Aneli [31]2 years ago
4 0

\huge \frak \green{question}

prove that √p is an irrational number , if p is not a perfect square.

\huge \frak \red{answer}

Let us assume, to the contrary, that √p is rational. So, we can find coprime integers a and b(b ≠ 0) such that :-

=> √p = a/b

=> √p b = a

=> pb² = a² ….(i) [Squaring both the sides]

=> a² is divisible by p

=> a is divisible by p So, we can write a = pc for some integer c.

Therefore,

a² = p²c² ….[Squaring both the sides]

=> pb² = p²c² ….[From (i)]

=> b² = pc²

=> b² is divisible by p

=> b is divisible by p

=> p divides both a and b.

=> a and b have at least p as a common factor.

But this contradicts the fact that a and b are coprime. This contradiction arises because we have assumed that √p is rational. Therefore, √p is irrational.

_____________________________________

\bold \green{i \: hope \: it \: is \: helpful}

________________________________

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dybincka [34]

Explicación paso a paso:

Debemos buscar el costo de cada boleto y la cantidad de personas que deben ir.

Dada la función que da forma al comportamiento expresado como;

f (x) = (-2x) ^ 2 + 80x + 300 donde;

x es el costo de cada boleto

f (x) es el número de personas que deben ir

Para obtener x, usaremos la expresión;

x = -b / 2a

De la ecuación cuadrática dada, a = -2, b = 80 yc = 300

Sustituir;

x = -80/2 (-2)

x = -80 / -4

x = 80/4

x = 20

Por lo tanto, el boleto cuesta $ 20.

Lo siguiente es obtener la cantidad de personas que deben ir. Para conseguirlo, sustituiremos x = 20 en la expresión modelada como se muestra;

f (x) = (-2x) ^ 2 + 80x + 300

f (20) = (-2 (20)) ^ 2 + 80 (20) +300

f (20) = (-40) ^ 2 + 1600 + 300

f (20) = 1600 + 1600 + 300

f (20) = 3500

Por lo tanto, 3500 personas tienen que ir

8 0
3 years ago
4) If a = 28 and b = 4, then a/b = ______
exis [7]

Answer:

7

Step-by-step explanation:

You divided both 28 and 4 and you will get 7 as your answer.

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3 years ago
Which of the following statements are true of the graph of the function f(x)=(x+5)(x-3)?
mr_godi [17]

Answers: b, d and e

b.The graph has a relative minimum

d. The graph has an x intercept at 3,0

e. the graph has an y intercept at 0,-15

f(x)=(x+5)(x-3)

The given equation is in the form of f(x) = a(x-b)(x-c)

If 'a' is positive then graph has a relative minimum

If 'a' is negative then graph has a relative maximum

Here a=1 that is positive so graph has a relative minimum .

To find x intercept we set f(x) =0 and solve for x

0=(x+5)(x-3)

x+5 =0 -> x = -5 so x intercept is (-5,0)

x - 3=0 -> x= 3 so x intercept is (3,0)

To find y intercept we plug in 0 for x

y=(x+5)(x-3)

y=(0+5)(0-3) = -15

so y intercept is (0,-15)



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