2017
Mathematics
67ca00ce0c643c71d77dee1f
If (2√3−√2)/(√3+2√2) = m + n √ 6, find the values of m and n respectively
A.
1, − 2
B.
− 2, n = 1
C.
−2/5 , 1
D.
2/3
Correct Answer: − 2, n = 1
Explanation
(2√3−√2)/(√3+2√2) = m + n √ 6 (2√3 − √2)/(√3 + 2√2) x (√3 − 2√2)/(√3 − √2) [2√3(√3 − 2√2) − √2(√3 − 2√2)]/[√3(√3 − 2√2) + 2√2(√3 − 2√2)] (2 × 3 − 4√6 − 6 + 2 × 2)/(3−2√6 + 2√6 − 4 × )2 = (6 − 4√6 − √6 + 4)/(3−8) =( 0−4√6 − 6)/5 = (10−5√6)/5 = − 2 + √6 ∴ m + n√6= − 2 + √6 m = − 2, n = 1
(2√3−√2)/(√3+2√2) = m + n √ 6 (2√3 − √2)/(√3 + 2√2) x (√3 − 2√2)/(√3 − √2) [2√3(√3 − 2√2) − √2(√3 − 2√2)]/[√3(√3 − 2√2) + 2√2(√3 − 2√2)] (2 × 3 − 4√6 − 6 + 2 × 2)/(3−2√6 + 2√6 − 4 × )2 = (6 − 4√6 − √6 + 4)/(3−8) =( 0−4√6 − 6)/5 = (10−5√6)/5 = − 2 + √6 ∴ m + n√6= − 2 + √6 m = − 2, n = 1THIS WEEK's
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