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Statement 1: n² - 6n = -9 This is a quadratic equation, so let's set it equal to zero: n² - 6n + 9= 0 Factor to get: (n - 3)(n - 3) = 0 So, n = 3 Since we know that n has only one value (n= 3), we can easily determine the value of (n + 1)² Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: (n - 1)² = n² - 5 Expand left side: n² - 2n + 1 = n² - 5 Subtract n² from both sides: -2n + 1 = -5 Subtract 1 from both sides: -2n = - 6 Solve: n = 3 Since we know that n has only one value (n= 3), we can easily determine the value of (n + 1)² Since we can answer the target question with certainty, statement 2 is SUFFICIENT
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