Question

What is the value of (2a+2b)/(2a-b), given that b ≠ 0 and (〖 a〗^2-ab+2b^2)/(a^2+ab+4b^2 )=1/3?

Answer 1

Given that (a² - ab + 2b²)/(a² + ab + 4b²) =1/3
On cross multiplying we get
  3a² - 3ab + 6b² = a² + ab + 4b²
⇒ 2a² - 4ab + 2b² = 0
on taking common factor 2 out we get
    a² - 2ab + b² = 0
⇒ (a - b)² = 0
⇒ a - b = 0
⇒ a = b.
now substituting a = b in
(2a + 2b )/(2a - b)
⇒(2a + 2a)/(2a -a)
= 4a/a
= 4

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