SOLUTION: difference of two natural no. are 4 and the sum of their square is 58 what the number

Question 669201: difference of two natural no. are 4 and the sum of their square is 58 what the number
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
difference of two natural no. are 4 and the sum of their square is 58 what the number
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Equations:
x - y = 4
x^2 + y^2 = 58
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Substitute for "x" and solve for "y":
(4+y)^2 + y^2 = 58
16 + 8y + 2y^2 = 58
y^2 + 4y -21 = 0
(y+7)(y-3) = 0
Natural Number solution:
y = 3
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Solve for "x"
x = 4+y
x = 7
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Cheers,
Stan H.
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Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

let's two natural no. be and
if difference of two natural no. are , we have
........eq. 1
and, if the sum of their square is we have
........eq. 2
solve the system:
........eq. 1
........eq. 2
_______________________________

........eq. 1..solve for
.....substitute in 2
.....solve for

.....solve quadratic

solutions:

and

now find :

and

so, you have two pairs of solutions:
and
or
and

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