The sum of the squares of two consecutive integers is 481. Find the integers​

{15, 16} or {-15, -16}

Step-by-step explanation:

Quick solution:

take half of the sum (approx. 240), sqrt(240)=15.5

So the numbers are 15 and 16.  and also the negative equivalents since squares are always positive.

Exact method:

Let

x=smaller integer,

x+1 = next integer.

sum:

x²⁺(x+1)^2 = 481

2x^2 + 2x + 1 = 481

2x^2 + 2x - 480 = 0

x^2 + x -240 = 0

x = 15 or x = -16

so the integers are

either

{15, 16} or {-15, -16}

Step-by-step explanation:

x2 + (x+1)2 =481

x2 + x2 + 2x +1 = 481

2x2 +2x - 480 = 0

2( x2 + x - 240) = 0

x2 + 16x - 15x - 240 = 0

(x+16) (x-15) = 0

x= -16 (ignore) ,       x= 15

1st integer = x = 15

2nd integer= x+1 = 15 +1 = 16