# The sum of the squares of three consecutive positive integers is 50.find the integers

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Let the three consecutive positive no`s be x, x + 1, x + 2

then the sum of the squares of the no`s = x² + (x + 1)² + (x + 2)² = 50 as given

x² + x² + 1 + 2x + x² + 4 + 4x = 50

⇒3x² + 6x + 5 = 50

⇒3x² + 6x = 45

⇒3x² + 6x - 45 = 0

⇒3x² -9x + 15x - 45 = 0

⇒3x(x - 3) + 15(x - 3) = 0

⇒(x - 3)(3x + 15) = 0

⇒x - 3 = 0 or 3x + 15 = 0

⇒x = 3 or 3x = -15

⇒x = 3 or x = -15/3 = -5

as the question describes the no`s as positive x =3 and not -5

∴x = 3 , x + 1 =4 , x+2 = 5

∴the no`s are 3,4,5.

then the sum of the squares of the no`s = x² + (x + 1)² + (x + 2)² = 50 as given

x² + x² + 1 + 2x + x² + 4 + 4x = 50

⇒3x² + 6x + 5 = 50

⇒3x² + 6x = 45

⇒3x² + 6x - 45 = 0

⇒3x² -9x + 15x - 45 = 0

⇒3x(x - 3) + 15(x - 3) = 0

⇒(x - 3)(3x + 15) = 0

⇒x - 3 = 0 or 3x + 15 = 0

⇒x = 3 or 3x = -15

⇒x = 3 or x = -15/3 = -5

as the question describes the no`s as positive x =3 and not -5

∴x = 3 , x + 1 =4 , x+2 = 5

∴the no`s are 3,4,5.

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Let one of the numbers = x

and other two numbers are = x-1 and x+1

(When you have to take three consecutive numbers, always choose x-1, x and x+1. calculations will become easy;)

sum of squares = 50

⇒ (x-1)² + x² + (x+1)² = 50

⇒ (x²-2x+1) + x² + (x²+2x+1) = 50

⇒ x²-2x+1 + x² + x²+2x+1 = 50

⇒ 3x² + 2 = 50

⇒ 3x² = 50-2 = 48

⇒ x² = 48/3 = 16

⇒ x = √16

⇒ x = 4

x-1 = 4-1=3

x+1=4+1=5

three numbers are 3,4,5

and other two numbers are = x-1 and x+1

(When you have to take three consecutive numbers, always choose x-1, x and x+1. calculations will become easy;)

sum of squares = 50

⇒ (x-1)² + x² + (x+1)² = 50

⇒ (x²-2x+1) + x² + (x²+2x+1) = 50

⇒ x²-2x+1 + x² + x²+2x+1 = 50

⇒ 3x² + 2 = 50

⇒ 3x² = 50-2 = 48

⇒ x² = 48/3 = 16

⇒ x = √16

⇒ x = 4

x-1 = 4-1=3

x+1=4+1=5

three numbers are 3,4,5