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Question
Solve for x:
22x+3 - 9 x 2x + 1 = 0
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Solution
22x+3 - 9 x 2x + 1 = 0
22x . 23 - 9 x 2x + 1 = 0
Put2x = t, so, 22x = t2
So, 22x . 23 - 9 x 2x + 1 = 0 becomes 8t2 - 9t + 1 = 0
⇒ 8t2 - 8t - t + 1 = 0
⇒ 8t(t - 1) - (t - 1) = 0
⇒ t - 1 = 0 or 8t - 1 = 0
⇒ t = 1 or t = `(1)/(8)`
⇒ 2x = 1 or 2x = `(1)/(2^3)`
⇒ 2x = 20 or 2x = 2-3
⇒ x = 0 or x = -3.
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