find two numbers which are reciprocals of each other and whose sum is 5
Involving systems of non linear equations
x = first nuber
y = 1 / x = reciprocal number
Systems of non linear equations is:
y = 1 / x
x + y = 5
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Replace y with 1 / x in second equation
x + 1 / x = 5
Multiply both sides by x
x^2 + 1 = 5 x
Subtract 5 x to both sides
x^2 - 5 x + 1 = 0
The solutions are:
x = ( 5 - √21 ) / 2
and
x = ( 5 + √21 ) / 2