Number Prob: 2 consec. pos. int's, so sum of squares is 85
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Re: Number Problems
Consecutive positive integers would be like 2, 3, 4 or 11, 12, 13. The important thing to note is that each one is one more than the one that comes before it.
Suppose you let x be the first of your positive integers.
Then, the next consecutive positive integer would be "one more" than x, or x + 1.
Now, the squares of these two integers are x<SUP>2</SUP> and (x + 1)<SUP>2</SUP>. And the problem says that "the sum of their squares is 85."
So.....
x<SUP>2</SUP> + (x + 1)<SUP>2</SUP> = 85
There's your equation....now it is up to you to solve it.
Katie1 said:
Consecutive positive integers would be like 2, 3, 4 or 11, 12, 13. The important thing to note is that each one is one more than the one that comes before it.
Suppose you let x be the first of your positive integers.
Then, the next consecutive positive integer would be "one more" than x, or x + 1.
Now, the squares of these two integers are x<SUP>2</SUP> and (x + 1)<SUP>2</SUP>. And the problem says that "the sum of their squares is 85."
So.....
x<SUP>2</SUP> + (x + 1)<SUP>2</SUP> = 85
There's your equation....now it is up to you to solve it.
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Re: Number Prob: 2 consec. pos. int's, so sum of squares is
Start trying pairs: 1 + 4 = 5: not a match; 4 + 9 = 13: not a match. And so forth.... :wink:
Eliz.
There aren't a whole lot of squares smaller than 85. You have 1, 4, 9, 16, 25, 36, 49, 64, and 81. Since the integers are right after each other, so will be their squares. So you need a pair of squares, one right after the other, that sum to eighty-five.Katie1 said:
Start trying pairs: 1 + 4 = 5: not a match; 4 + 9 = 13: not a match. And so forth.... :wink:
Eliz.
Re: Number Prob: 2 consec. pos. int's, so sum of squares is
x^2 + x^2 + 2x + 1 = 85
2x^2 + 2x + 1 = 85
x^2 + x - 84 = 0
The quadratic equation will tale you to the solution.
Easier yet, scanning a table of squares will quickly show you the answer.
x^2 + (x + 1)^2 = 85Katie1 said:
x^2 + x^2 + 2x + 1 = 85
2x^2 + 2x + 1 = 85
x^2 + x - 84 = 0
The quadratic equation will tale you to the solution.
Easier yet, scanning a table of squares will quickly show you the answer.
