Harvard University Insurance Policy expert Aptitude test

[@dan-florinchereches4892]

Raising to an power 1/(2x): X^1/x=√(5-24)=√(5+√(5^2-24))/2-√(5-√(5^2-24))/2=√3-√2 raising to power -1 (1/x)^(1/x)=1/(√3-√2) x=(√3-√2)^x if f(x)=x an increasing function and g(x)=(√3-√2)^x an exponential of exponent

[@walterwen2975]

Harvard University Insurance Policy expert Aptitude test: x² = (5 - √24)ˣ, x =? x² = (5 - √24)ˣ > 0, x > 0 x² = (5 - √24)ˣ = (5 - 4.899)ˣ = 0.101ˣ, (x²)¹⸍²ˣ = (0.101ˣ)¹⸍²ˣ, x¹⸍ˣ = 0.101¹⸍² = 0.318 Trial-and-error math to solve the equation, x = 1: x¹⸍ˣ = 1 > 0.318; 1 > x > 0, In-between x = 0.5: 0.5¹⸍⁰·⁵ = 0.250 < 0.318; 1 > x > 0.5, Close to 0.5 x = 0.54: 0.54¹⸍⁰·⁵⁴ = 0.319 > 0.318; 0.54 > x > 0.5, Slightly < 0.54 x = 0.539: 0.539¹⸍⁰·⁵³⁹ = 0.318 = 0.318; Proved The calculation was achieved on a smartphone with a standard calculator app Answer check: x = 0.539: x² = (5 - √24)ˣ; Confirmed as shown Final answer: x = 0.539