Determine two distinct real numbers a and b that satisfy this system of equations:
a
2-b = 73
b
2-a =73
a^2-b = 73
b^2-a = 73
a^2 - b^2 + (a-b) = 0
(a-b)(a+b+1) = 0
(a-b) is not zero since the 2 numbers are distinct
Therefore a+b+1 = 0 and b = -(a+1), substitute
a and b results will be interchangeable.
a^2 + a + 1 = 73
a^2 + a - 72 = 0
a = (-1 ± √289)/2
± one will be a, the other will be b.
√289 = 17
the + case:
a = 8
b = -9
a^2-b = b^2-a = 73
the - case:
a = -9
b = 8
which also checks.
{a,b} = {8, -9}
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Posted by Larry
on 2024-07-23 13:31:27 |
Analytic solution
