Question

Find the value of
$(\sqrt{3}+1)-(\sqrt{3}-1)^{4}$

Answer 1

Solution :

$(\sqrt{3}+1)^{4}-(\sqrt{3}-1)^{4}$

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We know that ,

i ) ( a + b )² - ( a - b )² = 4ab

ii ) ( a + b )² + ( a - b )² = 2( a² + b² )

iii ) a² - b² = ( a + b )( a - b )

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= [ (√3+1)²]² - [(√3-1)]²

= [(√3+1)² - (√3-1)²][(√3+1)² + (√3-1)² ]

= [4×(√3)×1] × { 2[(√3)² + 1²]}

= (4√3) × 2( 3 + 1 )

= (4√3) × 8

= 32√3

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