Question

The sum of the squares of five consecutive integers is 15. What are the integers?

Answer 1

Answer:

Let 5 consecutive integers be …..

(x-2), (x-1), x, (x+1), (x+2)

The sum of the squares of above nos..

(x-2)^2 +(x-1)^2 +x^2 +(x+1)^2 +(x+2)^2 = 15

=> {(x-2)^2 + (x+2)^2} + {(x-1)^2 + (x+1)^2} + x^2 = 15

=> {2x^2 + 8} + {2x^2 + 2} + x^2 = 15

=> 5x^2 + 10 = 15

=> x^2 + 2 = 3

=> x^2 = 1

=> x = +,- 1

If , x= -1

the consecutive integers are ….

-3, -2, -1, 0, 1 ……… Ans

& if, x= 1

the consecutive integers are ..

-1, 0, 1, 2, 3 ……….. Ans

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