Find three consecutive odd integers such that three times the product of the first and last integers, decreased by 150, is equal to the square of the second integer.

Solution

Solution

No Solution

Solution steps

Represent the numbers with

x

First number : x

Consecutive number 1 : x + 2

Consecutive number 2 : x + 4

A.T.Q.:

3 \dots - 150 = (x + 2)^{2}

Solve

3 \dots - 150 = (x + 2)^{2} : x = 3 \dots - 150 - 2, x = - 3 \dots - 150 - 2

Plug in

x = 3 \dots - 150 - 2 :

Invalid

Plug in

x = - 3 \dots - 150 - 2 :

Invalid

No Solution

Popular Examples

The sum of the ages of Bob and Cathy is 84 years. In 3 years, Bob will be twice as old as Cathy. How old is Cathy now?Hailey invested 1,700 in an account paying an interest rate of 2.2% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach 2,590?Enola is going to invest in an account paying an interest rate of 5.1% compounded continuously. How much would Enola need to invest, to the nearest cent, for the value of the account to reach 12,800 in 10 years?Levi is going to invest in an account paying an interest rate of 3.4% compounded continuously. How much would Levi need to invest, to the nearest ten dollars, for the value of the account to reach 620 in 16 years?one number is greater by 6 than twice another number but 3 times the smaller number exceeds the greater by 1. Find the numbers.