Find the fourth proportional of (x4 - y4), (x + y) and (x − y), provided x ≠ y.
(x2 + y2)-1
The correct answer is (x 2 + y 2 ) -1.
If x^2 - y^2 \ne 0, we can divide both sides by (x^2 - y^2): \[(x^2 + y^2) \times d = 1\] \[d = \frac{1}{x^2 + y^2}\] This confirms the previous result (x^2 + y^2)^{-1} and shows that using cross-multiplication is an equally valid approach. Problems involving fourth proportion often require a good grasp of algebraic factorization and manipulation skills to simplify expressions before finding the unknown term.
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