SOLUTION: The sum of the square of two number is 65 and the square of their sum is 121. Find the numbers
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Question 1105525: The sum of the square of two number is 65 and the square of their sum is 121. Find the numbers
please show workings Found 3 solutions by Alan3354, rothauserc, math_helper:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! The sum of the square of two number is 65 and the square of their sum is 121. Find the numbers
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Hint:
the square of their sum is 121 --> sum = 11 or -11
You can put this solution on YOUR website! 1) x^2 + y^ 2 = 65
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2) (x + y)^2 = 121
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using equation 2, square the left side of =
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3) x^2 + 2xy +y^2 = 121
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use equation 1 and substitute for x^2 + y^2 in equation 3
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2xy + 65 = 121
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2xy = 56
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xy = 28
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x = 28/y
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substitute for x in equation 1
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28^2/y^2 + y^2 = 65
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784 + y^4 = 65y^2
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let u = y^2, then
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u^2 -65u +784 = 0
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(u-16) * (u-49) = 0
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u = 16 or u = 49
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Note that u = y^2, so y = 4,-4 or 7,-7
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the numbers are 4 and 7 or -4 and -7
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You can put this solution on YOUR website! (1) (2)
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(2) —> —>
Substitute "11 - b" for "a" in (1):
or
b=4 —> a=7
Check: (ok) (ok)
b=7 —> a=4 (this is the same as above, the numbers are merely swapped)
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(2) also —> (a+b) = -11 —> a = -11 - b
Substitute "-11 - b" for "a" in (1):
or
b=-4 —> a=-11-(-4) = -7
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Check: (ok) (ok)
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Answer (two solutions):
(4 and 7) and
(-4 and -7)
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