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Question
Find the compounded ratio of the following:
(a2 - b2 ): (a2 + b2) and (a4 - b4 ): (a+ b)4
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Solution
Compounded ratio of (a2 -b2 ): (a2 + b2 )and(a4 -b4 ) : (a+ b)4
=`("a"^2 - "b"^2)/("a"^2 + "b"^2) xx ("a"^4 - "b"^4)/("a" + "b")^4`
= `(("a" + "b")("a" - "b"))/(("a"^2 + "b"^2)) xx (("a"^2 + "b"^2)("a"^2 - "b"^2))/ (("a" + "b")^2 ("a" + "b")^2)`
= `(("a" - "b")("a" + "b")("a" - "b")("a" +"b"))/(("a" + "b")^2 ("a" + "b")^2)`
= `("a - b")^2/("a + b")^2`
Compounded ratio= (a - b)2 : (a+ b)2
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