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NECO 2004 Mathematics · Question 1

Find x if (x - 2)2 = 179\frac{7}{9}

Options

  1. A.23\frac{2}{3} or 27\frac{2}{7}
  2. B.313\frac{1}{3} or 23\frac{2}{3}
  3. C.379\frac{7}{9} or 27\frac{2}{7}
  4. D.313\frac{1}{3} or 79\frac{7}{9}
  5. E.37\frac{3}{7} or 29\frac{2}{9}

Answer: B. 313\frac{1}{3} or 23\frac{2}{3}

Explanation written with AI and checked against the answer key

Analyze the question: We have (x − 2)² = 1 7/9, where "2" after the bracket is the square (the exponent). Concept: Convert the mixed number to an improper fraction, then take the square root of both sides. Remember that there are two roots, positive and negative. Solution: 1 7/9 = (9 + 7)/9 = 16/9 (x − 2)² = 16/9 Take the square root of both sides: x − 2 = ±4/3 Case 1: x − 2 = 4/3 x = 2 + 4/3 = 10/3 = 3 1/3 Case 2: x − 2 = −4/3 x = 2 − 4/3 = 2/3 So x = 3 1/3 or 2/3. Tip: Always convert mixed numbers to improper fractions before taking roots. Also never forget the ± when solving an equation of the form (x − a)² = k. Missing the second root is a common way students lose marks.

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