SOLUTION: Two no. Are like that if they are added the product is 56 and when they 2 no. Are added with their squares the sum is 128

Question 551045: Two no. Are like that if they are added the product is 56 and when they 2 no. Are added with their squares the sum is 128
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two no. Are like that if they are added the product is 56 and when they 2 no. Are added with their squares the sum is 128
:
I think you mean "When two numbers are multiplied the product is 56" and
When the squares are added the sum is 128
:
Let the two number be a & b
:
when multiplied: a*b = 56
When squares added: a^2 * b^2 = 128
we can rearrange this to
b^2 = 128 - a^2
b =
then from the 1st equation
a* = 56
square both sides
a^2(128-a^2) = 3136
128a^2 - a^4 = 3176
0 = a^4 - 128a^2 + 3136
Using the quadratic formula we get two solutions
a^2 = 33
a =
a = 5.746
and
a^2 = 95
a =
a = 9.746
:
a = 5.746, then b = 9.746
a = 9.746, then b = 5.746
:
:
Check this in the original problem
5.746 * 9.746 = 56.00
and
5.746^2 + 9.746^2 = 128.00
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