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The product of four consective integers is one less than a perfect square?
Suppose the smallest of the integers is n. Then the product of the four consecutive integers is n*(n+1)*(n+2)*(n+3) =(n2+3n)(n2+3n+2) = n4+6n3+11n2+6n So product +1 = n4+6n3+11n2+6n+1 which can be factorised as follows: n4+3n3+n2 +3n3+9n2+3n + n2+3n+1 =[n2+3n+1]2 Thus, one more that the product of four consecutive integers is a perfect square.
Product of three concecutive integer is 210 then find the sum of smallest two integers?
Let's assume that the three consecutive integers are n-1, n, and n+1. We know that their product is 210, so we can set up the equation (n-1)(n)(n+1) = 210. By solving this equation, we can find that the three integers are 6, 7, and 8. Therefore, the sum of the smallest two integers is 6 + 7 = 13.
Why is an odd number times an odd number an odd number?
Suppose m and n are integers. Then 2m + 1 and 2n +1 are odd integers.(2m + 1)*(2n + 1) = 4mn + 2m + 2n + 1 = 2*(2mn + m + n) + 1 Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + m + n is an integer - say k. Then the product is 2k + 1 where k is an integer. That is, the product is an odd number.
What is the integer if the product of two consecutive odd integers is one less than three times their sum?
Numbers are n and n + 2, so product = n2 + 2n and sum = 2n + 2. ie n2 + 2n + 1 = 6n + 6 or n2 - 4n - 5 = 0 Factors are (n + 1)(n - 5) making n = 5 and the integers 5 & 7. Check: 5 x 7 = 35; 5 + 7 = 36. OK There is also an answer of n = -1, making the integers -1 and 1, product being -1 and sum zero.
What is the link between the product of any four consecutive positive integers and some square numbers?
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
The product of two consecutive integers is 210?
You can solve this in two ways.1) Trial and error. That is, try multiplying two consecutive integers; if the product is too large, try smaller integers; if the product is too small, try larger consecutive integers. 2) Call the two consecutive integers "n" and "n+1", and solve the equation: n(n+1)=210
How do you find the product of consecutive integers?
Call the two consecutive integers n and n+1. Their product is n(n+1) or n2 +n. For example if the integers are 1 and 2, then n would be 1 and n+1 is 2. Their product is 1x2=2 of course which is 12 +1=2 Try 2 and 3, their product is 6. With the formula we have 4+2=6. The point of the last two examples was it is always good to check your answer with numbers that are simple to use. That does not prove you are correct, but if it does not work you are wrong for sure!
The product of four consective integers is one less than a perfect square?
Suppose the smallest of the integers is n. Then the product of the four consecutive integers is n*(n+1)*(n+2)*(n+3) =(n2+3n)(n2+3n+2) = n4+6n3+11n2+6n So product +1 = n4+6n3+11n2+6n+1 which can be factorised as follows: n4+3n3+n2 +3n3+9n2+3n + n2+3n+1 =[n2+3n+1]2 Thus, one more that the product of four consecutive integers is a perfect square.
Product of three concecutive integer is 210 then find the sum of smallest two integers?
Let's assume that the three consecutive integers are n-1, n, and n+1. We know that their product is 210, so we can set up the equation (n-1)(n)(n+1) = 210. By solving this equation, we can find that the three integers are 6, 7, and 8. Therefore, the sum of the smallest two integers is 6 + 7 = 13.
Why is an odd number times an odd number an odd number?
Suppose m and n are integers. Then 2m + 1 and 2n +1 are odd integers.(2m + 1)*(2n + 1) = 4mn + 2m + 2n + 1 = 2*(2mn + m + n) + 1 Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + m + n is an integer - say k. Then the product is 2k + 1 where k is an integer. That is, the product is an odd number.
What is the product of the integers from one to n?
It is n factorial, written as n!
What do you call the product of all positive integers from a given integer to 1?
For integers greater than 1 the product down to 1 is called factorial, indicated mathematically as N! wher N is the highest integer For example 5! = 5 factorial = 5x4x3x2x1 = 120
What is the integer if the product of two consecutive odd integers is one less than three times their sum?
Numbers are n and n + 2, so product = n2 + 2n and sum = 2n + 2. ie n2 + 2n + 1 = 6n + 6 or n2 - 4n - 5 = 0 Factors are (n + 1)(n - 5) making n = 5 and the integers 5 & 7. Check: 5 x 7 = 35; 5 + 7 = 36. OK There is also an answer of n = -1, making the integers -1 and 1, product being -1 and sum zero.
What is the link between the product of any four consecutive positive integers and some square numbers?
The product of four consecutive integers is always one less than a perfect square. The product of four consecutive integers starting with n will be one less than the square of n2 + 3n + 1
What are two consecutive integers have a product of 182?
One way to find out is write a formula. Let N and N+1 be the two integers, then N(N+1) = 182 N^2 + N - 182 = 0 This is a quadratic equation. If the factors are not obvious, (N -13)(N + 14) , then use the quadratic formula to find N. The factors tell you there are two possible solutions for N; 13 and -14. Now add 1 to these to get the two consecutive integers. 13 & 14 will work and -14 & -13 will work.
What is the product of all positive integers of 15?
The "integers of 15" appear to be '1' and '5'. Their product is 5 .
What are the integers if The sum of two integers is -1 the product of these integers is -56?
55
