SOLUTION: The sum of the square of two number is 65 and the square of their sum is 121. Find the numbers please show workings

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

Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
1) x^2 + y^ 2 = 65
:
2) (x + y)^2 = 121
:
using equation 2, square the left side of =
:
3) x^2 + 2xy +y^2 = 121
:
use equation 1 and substitute for x^2 + y^2 in equation 3
:
2xy + 65 = 121
:
2xy = 56
:
xy = 28
:
x = 28/y
:
substitute for x in equation 1
:
28^2/y^2 + y^2 = 65
:
784 + y^4 = 65y^2
:
let u = y^2, then
:
u^2 -65u +784 = 0
:
(u-16) * (u-49) = 0
:
u = 16 or u = 49
:
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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:

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

(1)
(2)
��
(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)
�
===
(2) also �> (a+b) = -11 �> a = -11 - b
Substitute "-11 - b" for "a" in (1):

or
b=-4 �> a=-11-(-4) = -7
�
Check:
(ok)
(ok)
================
Answer (two solutions):
(4 and 7) and
(-4 and -7)
================

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