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

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!

let's two natural no. be x and y
if difference of two natural no. are 4, we have
x-y=4........eq. 1
and, if the sum of their square is 58 we have
x%5E2%2By%5E2=58........eq. 2
solve the system:
x-y=4........eq. 1
x%5E2%2By%5E2=58........eq. 2
_______________________________

x-y=4........eq. 1..solve for x
x=y%2B4.....substitute in 2
%28y%2B4%29%5E2%2By%5E2=58.....solve for y
y%5E2%2B8y%2B16%2By%5E2=58
2y%5E2%2B8y%2B16=58
2y%5E2%2B8y%2B16-58=0
2y%5E2%2B8y-42=0.....solve quadratic
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A2%2A%28-42%29+%29%29%2F%282%2A2%29+
y+=+%28-8+%2B-+sqrt%28+64%2B336+%29%29%2F4+
y+=+%28-8+%2B-+sqrt%28+400%29%29%2F4+
y+=+%28-8+%2B-+20%29%2F4+
solutions:
y+=+%28-8+%2B+20%29%2F4+
y+=12%2F4+
highlight%28y+=3%29
and
y+=+%28-8+-20%29%2F4+
y+=-28%2F4+
highlight%28y+=-7%29

now find x:
x=y%2B4
x=3%2B4
highlight%28x=7%29
and
x=y%2B4
x=-7%2B4
highlight%28x=-3%29

so, you have two pairs of solutions:
highlight%28x=7%29 and highlight%28y+=3%29
or
highlight%28x=-3%29 and highlight%28y+=-7%29