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Question
Find the fourth proportion to the following :
(x2 - y2),(x3 + y3)anc(x3 - xy2 + x2y- y3)
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Solution
Let z be the fourth proportion
(x2 -y3) (x3 + y3) :: (x3 - xy2 + x2y - y3) : z
⇒ (x2 - y2 ) z = (x3 + y3)(x3- xy2 + x2y -y3)
⇒ z = `(("x"^3 + "y"^3)("x"^3 - "xy"^2 + "x"^2"y" - "y"^3))/("x"^2 - "y"^2)`
⇒ z = `(("x" + "y")("x"^2 - "xy"^2 + "x"^2"y" - "y"^3))/(("x + y")("x - y"))`
⇒ z = (x2 - xy + y2)(x + y)2
Therefore . the fourth proportion is (x2 + y2 - xy)(x + y)2
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