Question

The sum of the squares of the first two consecutive
numbers is equal to the square of the third number.

Answer 1

Step-by-step explanation:

And so we have found this algebraic formula for the sum of consecutive squares. 3(12 + 22 + 32 + . . .

Answer 2

SOLUTION

GIVEN

The sum of the squares of the first two consecutive

numbers is equal to the square of the third number.

TO DETERMINE

The number

EVALUATION

Let three numbers are a , a + 1 , a + 2

By the given condition

$\sf{ {a}^{2} + {(a + 1)}^{2} = {(a + 2)}^{2} }$

$\sf{ \implies {a}^{2} + {a}^{2} + 2a + 1 = {a}^{2} + 4a + 4}$

$\sf{ \implies {a}^{2} - 2a - 3 = 0}$

$\sf{ \implies {a}^{2} - (3 - 1)a - 3 = 0}$

$\sf{ \implies {a}^{2} - 3a + a - 3 = 0}$

$\sf{ \implies a(a - 3) + (a - 3 )= 0}$

$\sf{ \implies (a - 3) (a + 1 )= 0}$

a - 3 = 0 gives a = 3

a + 1 = 0 gives a = - 1

Taking a = 3 the numbers are 3 , 4 , 5

Taking a = - 1 the numbers are - 1 , 0 , 1

FINAL ANSWER

Hence the numbers are

3 , 4 , 5 OR - 1 , 0 , 1

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