find two numbers which are reciprocals of each other and whose sum is 5

Question

Involving systems of non linear equations

Answer 1

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