求 sqrt((2 + sqrt(3)) ^x) + sqrt((2 - sqrt(3) ^x) = 4 的所有解决方案.
然后,y=sqrt((2 + sqrt(3) ^x). 然后,sqrt(2 - sqrt(3) ^x) = sqrt(1 / 2 + sqrt(3) ^x) = 1/sqrt(2 + sqrt(3) ^x) = 1/sqrt(2 + sqrt(3) ^x) = 1/y,所以给出的方程变成 y + 1/y = 4. 然后,y^2 + 1 = 4y,或者 y^2 - 4y + 1 = 0. 根据正方程式,y = 2 ±sqrt(3). 因此,sqrt2 + sqrt(3) ^x) = 2 ±sqrt(3). 对于平方根,sqrt2 + sqrt(3) = 2 + sqrt(x) = 2 + sqrt3),所以 x = 2. 对于平方根,sqrt2 + sqrt(2 + sqrt(x) = 2 - 1/3) = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt3 - x - 2,所以,x = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt2 = sqrt3 - 2,