SOLUTION: whats 3 consecutive integers such that the sum of the squares of the smaller two is equal to the square of the largest

Question 288406: whats 3 consecutive integers such that the sum of the squares of the smaller two is equal to the square of the largest

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Recall that consecutive integers follow the pattern: x, x+1, x+2, ...

So the statement "3 consecutive integers such that the sum of the squares of the smaller two is equal to the square of the largest" means that

Start with the given equation.

FOIL

Combine like terms.

Get every term to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "x":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

This means that the numbers are either: 3, 4, 5

OR

the numbers are: -1, 0, 1
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