Question

The number (1+sqrt 5)/2 is known as the golden ratio, and shows up in various natural solutions. The ancient Greeks used this number as a guide in their architectural designs for the ratio of width to height for building fronts.

what is the conjugate expression for the golden ratio?

my answer is 1-sqrt of 5 but the book says (1-sqrt 5)/2..
can someone explain it to me..

Answer 1

(a+b)/b = b/a
just put b/a = x and solve for it's two values.

Answer 2

can explain further please?

Answer 3

(a+b)/b = b/a <-- definition of golden ratio
let b/a = golden ratio = x
a/b+b/b = x
1/(b/a) + 1 = x
1/x + 1 = x <--- quadratic equation ... which has two roots. find two roots. that's all.

Answer 4

the conjugate of 1+sqrt 5 is 1- sqrt 5

but they want the conjugate of (1+sqrt 5)/2

Answer 5

that's it? lol i need to read carefully.. thank you very much:)