SOLUTION: multiply any two consecutive numbers,then add the bigger number. use at least three examples. a) make a conjecture b) prove your conjecture

Question 1072494: multiply any two consecutive numbers,then add the bigger number. use at least three examples.
a) make a conjecture
b) prove your conjecture
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5*6 = 30 + 6 = 36 = 6^2

9 * 10 = 90 + 10 = 100 = 10^2

24 * 25 = 600 + 25 = 625 = 25^2

it appears that, if you multiply two consecutive numbers and then add the larger of the two, you will get the same result as if you squared the larger number.

this can be shown algebraically as follows:

a * (a + 1) + (a + 1) = a^2 + a + a + 1 = a^2 + 2a + 1.

factor a^2 + 2a + 1 and you will get (a + 1)^2.

RELATED QUESTIONS
multiply any two consecutive numbers then add the bigger number (answered by hkwu)

bob made the following conjecture:if you add three consecutive integers,then their sum is (answered by Edwin McCravy)

Pick a number and multiply it by 9. Add 15 to the product. Divided the sum by 3, end... (answered by math_helper)

# 7. Pick any number and multiply the number by 2. Add 10 to the product. Divide the... (answered by jim_thompson5910)

Follow the steps given, make a conjecture then prove your conjecture deductively: 1.... (answered by math_helper)

Follow the steps given, make a conjecture then prove your conjecture deductively: 1.... (answered by Edwin McCravy)

GIVEN THIS CONJECTURE; ANY TWO CONSECUTIVE SQUARE NUMBERS IS AN EVEN NUMBER. FIND THE... (answered by richard1234)

what are the examples of finding totals when we add any three consecutive even... (answered by macston,Alan3354)

One of the most famous unsolved problems in mathematics is a conjecture made by... (answered by solver91311)