Share
Notifications

View all notifications

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

Login
Create free account

Forgot password?
ConceptComponendo and Dividendo Properties

#### 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.

Is there an error in this question or solution?

#### APPEARS IN

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

#### Video TutorialsVIEW ALL [1]

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