Question

HOLA Guys !!
Question for uh....


Solve :-
(x-1)³ + 8 = 0



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Answer 1

Your answer is in the above of the attachment.................

Answer 2

Step-by-step explanation:

If we call any cube root of unity w , so that w3=1, we can write this as

(x−1)3=−8w3

Taking cube roots,

x−1=−2w

x=1−2w

There are three w s so there are three solutions:

w3−1=0

(w−1)(w2+w+1)=0

w=1 or w=−1±i3–√2

x=1−2w so x=−1 or x=2±i3–√

Check: Obviously x=−1 works. We’ll check one of the others:

(2−i3–√−1)3+8=(1−i3–√)(1−i3–√)2+8=(1−i3–√)(−2−2i3–√)+8=−8+8✓