Question

three consecutive even integers are such that the square of the thrid is 76 more than the square of the second. find the three integers.

Answer 1

Let the first even integer be : x

Other will be : (x + 2)

And third will be: (x + 4)

\[(x+4)^2 = 76 + (x+2)^2\]

\[(x+4)^2 - ( x+2 )^2 = 76\]

Solve for x now..

Answer 2

You can use the formula:

\[(a+b)^2 = a^2 + b^2 + 2ab\]

Answer 3

or we can call the middle one \(x\) since the first one does not enter in to the question
solve
\[x^2+76=(x+2)^2\]
\[x^2+76=x^2+4x+4\]
\[4x+4=76\]
\[4x=72\]
\[x=18\] so the three are \(\{16,18,20\}\) and the smallest one is 16

Answer 4

Is this a factoring method

Answer 5

no factoring needed for this problem

Answer 6

\[x^2+76=(x+2)^2\] looks like it might be a quadratic equation, but it is not one because there is an \(x^2\) on both sides, subtract it from both sides and you have a linear equation

Answer 7

No factoring method, x squared terms will automatically cancel each other you have to solve for x and constant terms...

Answer 8

just learning the quadratic formula trying to understand each method not to be confused. Thank you

Answer 9

Three consecutive odd integers are such that the square of the third integer is 33 less than the sum of the squares of the first two.

Answer 10

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 11

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 12

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 13

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 14

How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?

Details and assumptio

Answer 15

Three consecutive even integers are such that the square of the third is 64 more than the square of the first.

Answer 16

(PLEASE HELP)
Three consecutive odd integers are such that the square of the third integer I s9 less than the sum of the squares of the first two.

Answer 17

Prove by Induction
"The sum of the cube of any three consecutive integers is divisible by 9"

I confused with what is the basis step that I should take

Answer 18

What is the next step for this construction

Answer 19

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