Question

If 3ax + 2b² = 3bx + 2a², then express x in terms of a and b. Also, express the result in the simplest form.

Answer 1

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)