The sum of the roots of the equation 2 33 x - 2 + 2 11 x + 2 = 2 22 x + 1 + 1 is

Question

The sum of the roots of the equation 2 33 x - 2 + 2 11 x + 2 = 2 22 x + 1 + 1 is, 1 11, 2 11, 3 11, 4 11

MARKS App · Accepted Answer

Let, t = 2 11 x ⇒ 2 11 x 3 2 2 + 2 11 x . 2 2 = 2 11 x 2 . 2 + 1 ⇒ t 3 4 + 4 t = 2 t 2 + 1 ⇒ t 3 - 8 t 2 + 16 t - 4 = 0 Cubic in t has roots t 1 , t 2 , t 3 i.e. t 1 t 2 t 3 = 4 ⇒ 2 11 x 1 . 2 11 x 2 . 2 11 x 3 = 4 ⇒ 2 11 x 1 + x 2 + x 3 = 2 2 ⇒ 11 x 1 + x 2 + x 3 = 2 ⇒ x 1 + x 2 + x 3 = 2 11

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