JAMB 2017 Mathematics · Question 11
If = m + n √ 6, find the values of m and n respectively
Options
- A.1, − 2
- B.− 2, n = 1
- C., 1
- D.
Answer: B. − 2, n = 1
Explanation written with AI and checked against the answer key
Step 1: Analyze the question We need to rationalise the denominator, write the result in the form m + n√6, and read off m and n. Step 2: Concept Multiply the top and bottom by the conjugate of the denominator. The conjugate of (√3 + 2√2) is (√3 − 2√2). The denominator then becomes a difference of two squares: (a + b)(a − b) = a² − b². Step 3: Solution Denominator: (√3 + 2√2)(√3 − 2√2) = 3 − 4(2) = 3 − 8 = −5 Numerator: (2√3 − √2)(√3 − 2√2) = 2√3·√3 − 2√3·2√2 − √2·√3 + √2·2√2 = 6 − 4√6 − √6 + 4 = 10 − 5√6 So the fraction is: (10 − 5√6) / (−5) = −2 + √6 Comparing with m + n√6: m = −2, n = 1 Step 4: Answer This matches option B (−2, n = 1). Quick check: the left side is approximately (3.464 − 1.414)/(1.732 + 2.828) = 2.050/4.560 ≈ 0.450. The right side is −2 + 2.449 = 0.449. ✓ Exam tip: When you see a surd in the denominator of the form a + b, always multiply by the conjugate a − b. Watch the signs when expanding, because that is where most mistakes happen.AI can make mistakes. Report anything that looks wrong.
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