Asked by Aria
Two consecutive integers are squared. The sum of these squares of these squares is 545. What are the integers?
Answers
Answered by
MathMate
Fast way:
Half of 545 = 272 must fall between two perfect sequres, namely 256 and 289, which means that the integers are 16 and 17.
Standard way:
Let x be one of the integers, then x+1 is the other. So that:
x^2+(x+1)^2=545
2x^2+2x-544=0
x^2+x-272=0
(x+17)(x-16)=0
So x=16 or x=-17.
The consecutive integers are therefore:
16, 17, or
-17, -16
Half of 545 = 272 must fall between two perfect sequres, namely 256 and 289, which means that the integers are 16 and 17.
Standard way:
Let x be one of the integers, then x+1 is the other. So that:
x^2+(x+1)^2=545
2x^2+2x-544=0
x^2+x-272=0
(x+17)(x-16)=0
So x=16 or x=-17.
The consecutive integers are therefore:
16, 17, or
-17, -16
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.