solve √3-1-√3-1 by (√3)²-1²
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sitasahu0609gmailcom
28.06.2018
Math
Secondary School
+5 pts
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√3+1/√3-1=a-b√3 .. FIND A AND B.
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Panzer786
Panzer786 Genius
Heya !!!
✓3 + 1 / ✓3 - 1 = A - B✓3
LHS = ✓3+1/✓3-1
=> ✓3+1/✓3-1 × ✓3+1/✓3+1
=> (✓3 + 1 ) ( ✓3 + 1 ) / ( ✓3 + 1 ) ( ✓3 - 1)
=> (✓3+1)² / ( ✓3)² - (1)²
=> (✓3)² + (1)² + 2×✓3 + 1 / 3 - 1
=> 3 + 1 + 2✓3 / 2
=> 4+2✓3/2
=> 2 ( 2 + ✓3 ) / 2
=> 2+✓3
Now,
LHS = RHS
2 + ✓3 = A-B✓3
Clearly,
A = 2 and B = -1.
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