SOLUTION: Can you please help me find two consecutive positive integers that the sum of their squares is 85.

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Question 7575: Can you please help me find two consecutive positive integers that the sum of their squares is 85.
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive integers: x, x+1. Sum of their squares equal 85:
x%5E2%2B%28x%2B1%29%5E2=85
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=6,x=-7.
  • Graphical form: Equation x%5E2%2B%28x%2B1%29%5E2=85 was fully solved.
  • Text form: x^2+(x+1)^2=85 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%5E2%2B%28x%2B1%29%5E2=85+%29
    For tutors: simplify_cartoon( x^2+(x+1)^2=85 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%5E2%2B%28x%2B1%29%5E2=highlight_red%28+85+%29.
Moved these terms to the left highlight_green%28+-85+%29
It becomes x%5E2%2B%28x%2B1%29%5E2-highlight_green%28+85+%29=0.
Look at highlight_red%28+x%5E2%2B%28x%2B1%29%5E2-85+%29=0.
Equation highlight_red%28+x%5E2%2B%28x%2B1%29%5E2-85=0+%29 is a quadratic equation: 2*x^2+2*x-84 =0, and has solutions 6,-7
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=6,x=-7.

Universal Simplifier and Solver


Done!


-7 is not positive, so the solution that we are allowed to have is x=6, the next integer is 7. 6,7