Question

if x⁴+x²=1 then what is the value of x​

Answer 1

x^4 + x^2 = 1

x^4 + x^2 - 1 = 0

y^2 + y - 1 = 0

y^2 + y = 1

y^2 + y + 1/4 = 5/4

(y + 1/2)^2 = 5/4

y + 1/2 = sqrt(5)/2 or y + 1/2 = -sqrt(5)/2

y = sqrt(5)/2 - 1/2 or y + 1/2 = -sqrt(5)/2

x^2 = sqrt(5)/2 - 1/2 or y + 1/2 = -sqrt(5)/2

x = sqrt(sqrt(5)/2 - 1/2) or x = -sqrt(sqrt(5)/2 - 1/2) or y + 1/2 = -sqrt(5)/2

x = sqrt(sqrt(5)/2 - 1/2) or x = -sqrt(sqrt(5)/2 - 1/2) or y = -1/2 - sqrt(5)/2

x = sqrt(sqrt(5)/2 - 1/2) or x = -sqrt(sqrt(5)/2 - 1/2) or x^2 = -1/2 - sqrt(5)/2

Answer: x = sqrt(sqrt(5)/2 - 1/2) or x = -sqrt(sqrt(5)/2 - 1/2) or x = i sqrt(1/2 + sqrt(5)/2) or x = -i sqrt(1/2 + sqrt(5)/2)