Question

(x^2+2x-15)^5=1 find x​

Answer 1

Answer:

solved below

Step-by-step explanation:

(x^2+2x-15)^5 = 1

(x^2+2x-15)^5 = e∧2πi  , e = Euler's number , i =√-1

The number 1 has 5 different nth roots in the complex plane, namely

1,ω,ω²,ω³,ω∧4

ω= e∧iπ/5

ω²= e∧2iπ/5

ω³= e∧3iπ/5

ω∧4= e∧4iπ/5

now taking the real root 1

x^2+2x-15 = 1

x^2+2x-14 = 0

x = -2 ± 10√2 ÷2

x = -1 ± 5√2

we can repeat the procedure with other ω's