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Question
If 3ax + 2b2 = 3bx + 2a2, then express x in terms of a and b. Also, express the result in the simplest form.
Solution
3ax + 2b2 = 3bx + 2a2
⇒ 3ax - 3bx = 2a2 - 2b2
⇒ x(3a - 3b) = 2a2 - 2b2
⇒ x = `(2"a"^2 - 2"b"^2)/(3"a" - 3"b")`
⇒ x = `(2("a"^2 - "b"^2))/(3("a"- "b")`
⇒ x = `(2("a" + "b")("a" - "b"))/(3("a" - "b")`
⇒ x = `(2("a" + "b"))/(3)` ....(∵ a ≠ b)
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