# SOLUTION: Please help: i just can't figure these two questions out: #1 Find two negative consecutive integers such that the square of the larger diminished by five times the smaller is equ

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 Question 175265: Please help: i just can't figure these two questions out: #1 Find two negative consecutive integers such that the square of the larger diminished by five times the smaller is equal to 71. #2 find three consecutive odd integers such that the square of the second integer exceeds the largest integer by 10. thank you - desperatly seeking help :)Answer by gonzo(654)   (Show Source): You can put this solution on YOUR website!problem number 1: --- let x = first negative integer let x + 1 = second negative integer. --- the problem states that the square of the larger minus 5 times the smaller is equal to 71. --- this means that (x+1)^2 - 5x = 71 which means that x^2 + 2x + 1 - 5x = 71 which means that x^2 - 3x + 1 = 71 which means that x^2 - 3x - 70 = 0 which means that (x-10) * (x+7) = 0 which means that x = 10 or x = -7 --- since the number is negative, x = -7 is the only applicable answer. --- to prove, substitute in original equation. --- the numbers are x and x+1 which means that the numbers are -7 and -6. -6 is the larger number. square of the larger number minus 5 times the smaller number is 71. (-6)^2 - (5*(-7)) = 36 - (-35) = 36 + 35 = 71. --- x = -7 checks out ok. --- answer is the 2 negative consecutive numbers are -7 and -6. --- problem number 2: --- let x = one of the negative numbers, then x + 2 = next negative number, and x + 4 = next negative number. --- largest negative number is x + 4 middle negative number is x + 2 smallest negative number is x --- problem states that the square of the middle negative number is greater than the largest negative number by 10. this means that (x+2)^2 = (x+4) + 10 which means that x^2 + 4x + 4 = x + 14 which means that x^2 + 3x - 10 = 0 which means that (x+5) * (x-2) = 0 which means that x = -5 or x = 2 --- since the number has to be negative, then x = -5 is the only applicable answer to the problem. --- if x = -5, then x + 2 = -3, and x + 4 = -1 --- largest number is -1 middle number is -3 --- square of second number is 9 largest number + 10 is 9 square of second number equals the largest number plus 10 which satisfies the problem statement. --- answer is the 3 negative consecutive numbers are: -5, -3, -1 ---