Geometric mean (1 Viewer)

[lsdpoon1337]

Can someone help me to this question

Let triangle ABC be 90 degrees at C, so a^2 + b^c= c^2, find the ratio of c:a if:

b is the geometric mean of a and c.




Thanks

 

[dp624]

cos b is the GM of a and c
this means that b = SQRT(ac)
b^2 = ac

so ac = a^2 + c^2

divide both sides by a^2

c/a = 1 + c^2/a^2

let c/a = x

so x = 1 + x^2

solve by quadration equation

x^2 - x +1 =0

blah, you can do the rest

 

[lsdpoon1337]

Cheers, thanks for help