Two equations

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	Hi My name is Jennifer a student in year 11. The following problems have me stuck and any help would be greatly appreciated seeing my text book is doing me no favours: 3^2a+1 - 283^a + 9=0 and 5^2m - 5^m=20 Thankyou for your time Jennifer Hi Jennifer, Mny times solving an angebra problem is seeing a pattern. In your second problem 5^2m is the square of 5^m, so the pattern I see is (something squared) - (something) = 20 To use more conventional mathematical notation, let x = 5^m, then the expression is x² - x = 20 That is x² - x - 20 = 0 which factors to give (x - 5)(x + 4) = 0 and hence x = 5 or x = -4. Since x = 5^m and 5^m cannot be negative, the only solution is 5^m = 5 and thus m = 1. Can you now solve the first problem? Penny
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