SOLUTION: four consecutive positive integers. The sum of the squares of the second and third is 61. Find the integers.

Question 830477: four consecutive positive integers. The sum of the squares of the second and third is 61. Find the integers.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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u = x + 3
z = x + 2
y = x + 1
yy + zz = 61
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(x + 1)(x + 1) + (x + 2)(x + 2) = 61
xx + 2x + 1 + xx + 4x + 4 = 61
2xx + 6x - 56 = 0
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the above quadratic equation is in standard form, with a=2, b=6, and c=-56
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 6 -56
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 4
x = -7
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the negative root doesn't fit the problem statement, so use the positive root
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x = 4
y = 5
z = 6
y = 7
---
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---
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---
Solve systems of linear equations up to 6-equations 6-variables:
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