Question

$frac{1}{sqrt{sqrt{23}+4 }-1 }$ - $frac{1}{sqrt{sqrt{23}+4 }+1 }$

Answer 1

a² - b² = (a - b)(a + b)

1/(√(√23 + 4) - 1) - 1/(√(√23 + 4) + 1) = к общему знаменателю) =

= [(√(√23 + 4) + 1) - (√(√23 + 4) - 1)]/(√(√23 + 4) - 1)(√(√23 + 4) + 1) =

= 2/(√23 + 3) = долножаем числитель и знаменатель на (√23 - 3) =

= 2(√23 - 3)/(√23 + 3)(√23 - 3) = 2(√23 - 3)/(23 - 9) = 2 (√23 - 3)/14 =

= (√23 - 3)/7