Harvard University Pure Mathematics Admission Interview

[@wes9627]

Recognize this as a Golden Ratio problem and solve easily. Divide the given equation by (60)^{1/√x): (3/2)^{1/√x)-1=(2/3)^{1/√x). Substitute Φ=(3/2)^{1/√x) to obtain Φ-1=1/Φ. Then multiply by Φ and rearrange to Φ^2-Φ-1=0, which is the Golden Ratio equation. The positive root of this equation is the Golden Ratio Φ=(√5+1)/2=(3/2)^{1/√x). It follows that √x=ln(3/2)/lnΦ and x=[ln(3/2)/lnΦ]^2=0.709960837243671

[@派遣配管]

Equation in thumbnail is not correct! Disgusting.

[@prollysine]

let u=(3/2)^(1/Vx) , Vx=log(3/2)/log((-1+V3)/2) , test , 90^(1/Vx)+ 60^(1/Vx)=~ 0.1255 , 40^(1/Vx)=~ 0.1255 , OK , solu , x=((og(3/2)/log((-1+V5)/2))^2 , x=~ 0.709961 , / Vx=~ -0.842592 / ,