Solve: 5^(x + 1) + 5^(2 − x) = 5³ + 1

Question

KnowledgeBoat · Accepted Answer

Given, 5x+1 + 52-x = 53 + 1 ⇒ 5x.51 + 52.5-x = 125 + 1 ⇒ 5x.51 + = 126 Let 5x be y. ⇒ 5y + = 126 ⇒ 5y2 + 25 = 126y ⇒ 5y2 - 126y + 25 = 0 ⇒ 5y2 - 125y - y + 25 = 0 ⇒ 5y(y - 25) - (y - 25) = 0 ⇒ (y - 25)(5y - 1) = 0 ⇒ (y - 25) = 0 or (5y - 1) = 0 ⇒ y = 25 or y = ⇒ y = 52 or y = 5-1 Substituting the value of y, ⇒ 5x = 52 or 5x = 5-1 ⇒ x = 2 or -1 Hence, the value of x = 2 or -1.

Mathematics

Solve: 5^x+1 + 5^2-x = 5³ + 1

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Solve: 5x+1 + 52-x = 53 + 1

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