3x + 2 + 3-x = 10

1.	3x + 2 + 3-x = 10
Answer» 3^x + 2 + 3^-x = 10 ⇒ 3^x + 3^-x - 8 = 0 ⇒ 3^2x + 1 - 8 x 3^x = 0 ⇒ (3^x)² - 8 x 3^x + 1 = 0 which is a quadratic equation in 3^x. ∴ 3^x = \(\frac{-(-8)\pm\sqrt{64-4}}{2}=\frac{8\pm\sqrt{60}}{2}=\frac{8\pm2\sqrt{15}}{2}\) = 4±√15 ⇒ x = log₃ (4+√15) or x = log₃ (4-√15).

Answer»

3^x + 2 + 3^-x = 10

⇒ 3^x + 3^-x - 8 = 0

⇒ 3^2x + 1 - 8 x 3^x = 0

⇒ (3^x)² - 8 x 3^x + 1 = 0 which is a quadratic equation in 3^x.

∴ 3^x = \(\frac{-(-8)\pm\sqrt{64-4}}{2}=\frac{8\pm\sqrt{60}}{2}=\frac{8\pm2\sqrt{15}}{2}\) = 4±√15

⇒ x = log₃ (4+√15) or x = log₃ (4-√15).

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3x + 2 + 3-x = 10

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