Question

• (a+b) +(aw+bw^2)+(aw^2+bw)

Answer 1

Answer:

Answer is in the attachment

Answer 2

Answer:

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If a= -b this is clearly true for any w. Suppose a ≠ -b; then you can divide both sides by (a+b), resulting in:

a2w3+b2w3+abw4+abw2=a2−ab+b2

Comparing coefficients for a2,b2,ab between LHS and RHS, we note that the identity holds if, simultaneously, w3=1 and w4+w2=−1

⟹w×1+w2=−1⟹w2+w+1=0⟹w=−1±i3–√2