Question

The sum of squares of two consecutive negative integers is 61

Answer 1

Correct Question-

The sum of squares of two consecutive negative integers is 61. Find the two negative integers.

Answer: -6, -5

Step by step explanation:

Suppose that 'n' is a negative number.

Thus, (n - 1) is a consecutive negative number of 'n'

As per your question,

(n - 1)² + n² = 61.. (eq.1)

n² - 2n + 1 + n² = 61

2n² - 2n - 60 = 0

n² - n - 30 = 0

(n - 6)(n + 5) = 0

n = 6 or n = -5

As per the question, the number is negative,

So, n ≠ 6

n = -5

Substituting n = -5 in (eq.1) and simultaneously verifying the equation.

(-5 - 1)² + (-5)² = 61

(-6)² + 25 = 61

36 + 25 =61

Answer: -6, -5