а) 1/(4+2√3) +1/(4-2√3) = (4-2√3+4+2√3)/(4+2√3)(4-2√3) =8/(4² -(2√3)²)=8/4 =2.
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б) ∛(5 -2√6) *∛(5+2√6) = ∛(5 -2√6) *∛(5+2√6) =∛(5 ² -(2√6)²) =∛(25 -24) =1.
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а) √(a² +8a +16) -|a+4| -8 =√(a+4)² -|a+4| -8 = |a+4| -|a+4| -8 = - 8.
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б) 11(6^1/2 -√3)²/12(3 -2*2^(1/2)) =11(√6 -√3)²/(2 -2√2*1 +1) =11*(√3(√2 -1))²/(√2 -1)² =11*3 =33.
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в) (1/(√a +√(a+1)) +1/(√a -√(a+1) : (1+√((a+1)/(a-1) )=
( √a -√(a+1)+ √a +√(a+1)/ (√(a +√(a+1)(√a -√(a+1) :(√(a-1) +√(a-+1))√(a-1) =
2√a/(a- (a+1)) * √(a-1)/(√(a-1) +√(a+1)) = - 2√(a(a-1))/(√(a-1) +√(a+1)) =
= 2√(a(a-1))*(√(a+1) -√(a-1)) )/(√(a+1) +√(a-1)) (√(a+1) +√(a-1)) =
=2√(a(a-1))*(√(a+1) -√(a-1)) )/2 = √(a(a-1))*(√(a+1) -√(a-1)).