SOLUTION: 1. The product of two consecutive odd numbers is 10 more than the square of the smaller number. 2. If three times the smaller of two consecutive even integers is added to the l

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Question 187218: 1. The product of two consecutive odd numbers is 10 more than the square of the smaller number.
2. If three times the smaller of two consecutive even integers is added to the larger, the result is 4 more than three times the larger.
3. The product of two consecutive even numbers is 12 more than the square of the smaller number.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


1. The product of two consecutive odd numbers is 10 more than the square of the smaller number.
Consecutive Odd numberssystem%28x=smaller%2Cx%2B2=bigger%29
Then,%28x%29%28x%2B2%29=x%5E2%2B10, EQN 1
x%5E2%2B2x=x%5E2%2B10--->
red%28x=5%29, Smaller Number
5%2B2=red%287%29, Bigger Number
Go back EQN 1 ---->5%2A7=5%5E2%2B10--->35=25%2B10--->35=35

2. If three times the smaller of two consecutive even integers is added to the larger, the result is 4 more than three times the larger.
Consecutive Even numberssystem%28x=smaller%2Cx%2B2=bigger%29
Then,highlight%283x%29%2Bx%2B2=4%2Bhighlight%283%28x%2B2%29%29, EQN 2
4x%2B2=4%2B3x%2B6---->4x-3x=4%2B6-2
red%28x=8%29, Smaller Number
Also, 8%2B2=red%2810%29, Bigger number
Go back EQN 2 ----->3%2A8%2B8%2B2=4%2B3%288%2B2%29---->24%2B10=4%2B3%2810%29-->34=4%2B30--->34=34

3. The product of two consecutive even numbers is 12 more than the square of the smaller number.
Consecutive Even Numebrssystem%28x=smaller%2Cx%2B2=bigger%29
Then,%28x%29%28x%2B2%29=12%2Bx%5E2, EQN 3
x%5E2%2B2x=12%2Bx%5E2---->
red%28x=6%29, Smaller number
Also,6%2B2=red%288%29, Bigger Number
Go back EQN 3 ----> %286%29%288%29=12%2B6%5E2---->48=12%2B36--->48=48

Thank you,
Jojo