contestada

The sum of the square of a positive number and the square of 3 more than the number is 45. what is the​ number?

Respuesta :

Americ
x= a number

sum= add
more than= add
is= equal sign
square of= multiply the # by itself

x^2 + (x+3)^2= 45
x^2 + (x+3)(x+3)= 45

x^2 + x^2 + 3x + 3x + 9 = 45
combine like terms

2x^2 + 6x + 9= 45
subtract 9 from both sides

2x^2 + 6x= 36
reduce by dividing everything by 2

x^2 + 3x= 18
subtract 18 from both sides

x^2 + 3x - 18= 0
factor
(x+6)(x-3)= 0

x+6= 0
x= -6

x-3=0
x= 3

The question asks for the POSITIVE integer, so...

ANSWER: x= 3

Hope this helped! :)
fichoh

The positive integer is [tex]3[/tex]

Let the number be [tex]a[/tex]

square of [tex]a = a^{2}[/tex]

Square of [tex]3[/tex] more than [tex]a[/tex] = [tex](3+a)^{2}[/tex]

[tex](3 + a)^{2} = (3+a)(3+a) = 9 + 3a + 3a + a^{2} = a^{2} + 6a + 9[/tex]

[tex]a^{2} + a^{2} + 9a + 9 = 45[/tex]

[tex]2a^{2} + 6a + 9 = 45[/tex]

Subtract 9 from both sides :

[tex]2a^{2} + 6a = 45 - 9[/tex]

[tex]2a^{2} + 6a = 36[/tex]

Divide through by 2

[tex]a^{2} + 3a = 18\\a^{2} + 3a - 18 = 0[/tex]

Factorize :

[tex]a^{2} + 6a - 3a - 18 = 0\\a(a + 6) - 3(a + 6) = 0\\a + 6 = 0\\or\\a - 3 = 0[/tex]

[tex]a = 3 ;\\or\\a = - 6[/tex]

since, a is a positive integer, then [tex]a = 3[/tex]



Learn more : https://brainly.com/question/18796573

Learn more : https://brainly.com/question/18796573