One integer is 2 less than another. The sum of their squares is 34. Find the integers.
2 answers
Write the squares of 2 through 7.
The 1st integer = X.
The 2nd integer = x - 2.
x^2 + (x-2)^2 = 34.
x^2 + x^2 - 4x + 4 = 34,
2x^2 - 4x + 4 = 34,
2x^2 - 4x - 30 = 0,
x^2 - 2x - 15 = 0, -15 = -5 * 3. sum = -5 +3 = -2 = B.
(x-5)(x+3) = 0,
x - 5 = 0. X = 5.
x + 3 = 0. X = -3.
X = 5(chose positive value) = 1st integer
x-2 = 5-2 = 3 = 2nd integer.
The 2nd integer = x - 2.
x^2 + (x-2)^2 = 34.
x^2 + x^2 - 4x + 4 = 34,
2x^2 - 4x + 4 = 34,
2x^2 - 4x - 30 = 0,
x^2 - 2x - 15 = 0, -15 = -5 * 3. sum = -5 +3 = -2 = B.
(x-5)(x+3) = 0,
x - 5 = 0. X = 5.
x + 3 = 0. X = -3.
X = 5(chose positive value) = 1st integer
x-2 = 5-2 = 3 = 2nd integer.
5 answers