Question

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What will be the value of n in the expression (wy)n-2 = (y/x)n-5?​

Answer 1

Answer:

Down vote

Accepted

Hint: Apply Theorem 1.2 to xy.

Edit: It follows from Theorem 1.2 that (xy)n−1=(xy−1)((xy)n−1+⋯+xy+1).

Now multiply the equation by yn to get

yn((xy)n−1))=yn(xy−1)((xy)n−1+⋯+xy+1)

Simplifying on the left-hand side and rewritting yn as yyn−1 on the right-hand side we get

(xn−yn)=yyn−1(xy−1)((xy)n−1+⋯+xy+1)

Because the product is commutative you can rewrite the right-hand side to get

(xn−yn)=y(xy−1)yn−1((xy)n−1+⋯+xy+1)

Finally, on the right-hand side, factor in y and yn−1 accordingly to get

(xn−yn)=(x−y)(xn−1+⋯+xyn−2+yn−1)

Step-by-step explanation:

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