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The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 times the square of the smaller one. Find the integers?
Let lowest number be n. The larger numbers are n + 2 and n + 4.
So 4n2 = (n + 2)2 + (n + 4)2 + 12
= n2 + 4n + 4 + n2 + 8n + 16 + 12
= 2n2 + 12n + 32
So 4n2 - 2n2 - 12n - 32 = 0
ie 2n2 - 12n -32 = 0
which factorises as (2n - 16)(n + 2)
The positive solution is thus n = 16/2 = 8 and the other numbers are 10 & 12.
What else can I help you with?
What are two consecutive integers such that the smaller added to two times the larger gives a sum of 16?
There are no such integers.
When the smaller of two consecutive integers is added to five times the larger the result is 65?
The integers are 10 and 11.
The larger of two consecutive integers is represented by x plus 4 Which expression represents the smaller integer?
x+3 and x+4 would be consecutive integers.
What is the largest of 3 consecutive negative integers if the product of the larger two integers is 5 more than the smaller integer?
-1
Find two consecutive integers such that the larger is nine more than twice the smaller?
-10 and -11.
Find two consecutive even integers so that three times the smaller is 40 mor than two time the larger?
There are no two consecutive even integers, consecutive odd integers, or consecutive integers that satisfy that relationship.
What are two consecutive integers such that the smaller added to two times the larger gives a sum of 16?
There are no such integers.
The sum of two consecutive odd integers is 156 what is the larger integers?
Divide the sum of the two consecutive odd integers by 2: 156/2=78. The two consecutive odd integers will be one more and one less than 78, so the smaller will be 77 and the larger will be 79.
When the smaller of two consecutive integers is added to five times the larger the result is 65?
The integers are 10 and 11.
When the smaller of two consecutive integers is added to three times the larger the result is 51. Find the integers?
12 and 13.
The sum of two consecutive even integers is 58what is the larger integer?
The larger integer is 30. The smaller is 28.
The larger of two consecutive integers is represented by x plus 4 Which expression represents the smaller integer?
x+3 and x+4 would be consecutive integers.
Find two consecutive integers whose sum is eighty nine let x be the smaller of these two integers what is the larger of these two consecutive integers what r the two numbers?
44 & 45
What is the largest of 3 consecutive negative integers if the product of the larger two integers is 5 more than the smaller integer?
-1
Find two consecutive integers such that the larger is nine more than twice the smaller?
-10 and -11.
What are consecutive square numbers?
Consecutive square numbers are the squares of consecutive integers. For example, if you take the integers 1, 2, and 3, their squares are 1² = 1, 2² = 4, and 3² = 9, making 1, 4, and 9 consecutive square numbers. These square numbers differ by an increasing odd number: 4 - 1 = 3 and 9 - 4 = 5. Thus, the pattern continues as you square larger consecutive integers.
What are two consecutive even integers such that the square off the smaller is 10 more than the larger?
4 and 6
