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Another Four Reals (Posted on 2024-01-17)

If a, b, c, and d are real numbers, then find a, b, c, and d.

a + 1/b = 1
b + 1/c = 2
c + 1/d = 3
d + 1/a = 4

Modification of a problem seen on SyberMath's youtube channel

No Solution Yet Submitted by Larry

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Solution

| Comment 1 of 2

By straightforward substitutions:

B=1/(1-A)

D=4-1/A

C=3-1/D=3-1/(4-1/A)

B=2-1/C=2-1/(3-1/D)=2-1/(3-1/(4-1/A))

1/(1-A)=2-1/(3-1/(4-1/A))

(1-A)/(1-2A)=3-1/(4-1/A)

(2-5A)/(1-2A)=1/(4-1/A)

(1-2A)=(4-1/A)(2-5A)

A-2A^2=(4-A)(2-5A)

18A^2-12A+2=0

A=1/3

B=3/2

C=2

D=1

Posted by Jer on 2024-01-17 13:48:24

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