Question

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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Answers

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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