Question

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

Answer 1

Answer:

The integers are 3,4 and 5

3 square plus 4 square plus 5 square =

9+16+25=50

Answer 2

Answer:

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Step-by-step explanation:

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

⇒(x - 3) (x + 5) = 0

⇒x = 3 or x = -5

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

∴ x = 3 , x + 1 =4 , x+2 = 5

∴ The consecutive no`s are 3,4,5.