Solve for x: √(x + 6√2) − √(x − 6√2) = 2√2
Question:
Solve for x: √(x + 6√2) − √(x − 6√2) = 2√2
Solve for x: √(x + 6√2) − √(x − 6√2) = 2√2
Options
Answer: 11
Explanation:
Solution: Let: a = √(x + 6√2) b = √(x − 6√2) Then: a − b = 2√2 a² − b² = (x + 6√2) − (x − 6√2) = 12√2 Use a² − b² = (a − b)(a + b): 12√2 = (2√2)(a + b) → a + b = 6 Solve system: a − b = 2√2 a + b = 6 Add: 2a = 6 + 2√2 → a = 3 + √2 Then: b = 6 − a = 3 − √2 Find x: x + 6√2 = a² = (3 + √2)² = 9 + 6√2 + 2 = 11 + 6√2 x = 11
Explanation:
Solution: Let: a = √(x + 6√2) b = √(x − 6√2) Then: a − b = 2√2 a² − b² = (x + 6√2) − (x − 6√2) = 12√2 Use a² − b² = (a − b)(a + b): 12√2 = (2√2)(a + b) → a + b = 6 Solve system: a − b = 2√2 a + b = 6 Add: 2a = 6 + 2√2 → a = 3 + √2 Then: b = 6 − a = 3 − √2 Find x: x + 6√2 = a² = (3 + √2)² = 9 + 6√2 + 2 = 11 + 6√2 x = 11
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