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If a : B = C : D , Then Prove that (A2 + Ab + B2)/(A2 - Ab + B2) - ICSE Class 10 - Mathematics

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Question

If a : b = c : d , then prove that `("a"^2 + "ab" +
"b"^2)/("a"^2 - "ab" + "b"^2) = ("c"^2 + "cd"+ "d"^2)/("c"^2 - "cd" + "d"^2)`

Solution

`"a"/"b" = "c"/"d" => "a" = "bc"/"d"`

LHS

`("a"^2 + "ab" + "b"^2)/("a"^2 - "ab" + "b"^2)`

`= (("bc"/"d")^2 + ("bc"/"d")"b" + "b"^2)/(("bc"/"d")^2 - ("bc"/"d")"b" + "b"^2)`

`= ("b"^2"c"^2 + "b"^2"cd" + "d"^2"b"^2)/("b"^2"c"^2 - "b"^2 "cd" + "d"^2"b"^2)`

`= ("b"^2("c"^2 + "cd" + "d"))/("b"^2("c"^2 - "cd" + "d"^2)) = ("c"^2 + "cd" + "d"^2)/("c"^2 - "cd" + "d"^2)` = RHS

LHS = RHS

Hence , proved.

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 5

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Solution If a : B = C : D , Then Prove that (A2 + Ab + B2)/(A2 - Ab + B2) Concept: Componendo and Dividendo Properties.
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