185 а) В=(1-d^(-1/4))*(d^(1/2) +d^(1/4))*(d^(1/2) +1) =
(d^(1/4)-1)* (d^(1/4) +1)*(d^(1/2) +1) =(d^(1/2) -1)*(d^(1/2) +1) =d - 1 .
при d=3 ⇒В =2.
* * * d^(1/2) +d^(1/4) =d^(1/4)*(d^(1/4) +1) и d^(1/4)*(1-d^(-1/4)) =d^(1/4) -1 * * *
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186 б) В= (c^(2/3) +c^(1/3))* (c^(1/3) - 1+ c^(-1/3)) =
(c^(1/3) +1)*c^(1/3)* (c^(1/3) - 1+ c^(-1/3)) = (c^(1/3) +1)*(c^(2/3) - c^(1/3)+ 1) =
c +1. при c=3 ⇒В =4.
* * * (a+b)(a² -ab +b²) =a³ +b³ || a =a^(1/3) =∛a ; b =1 || * * *
189 а) В= a^(-1/2) +( a^(-1/2) - a^(1/2) ) /(a+a^(1/2))
= 1/√a +( 1/√a - √a ) /√a(√a+1) =(√a+1 +1/√a -√a) /√a(√a+1) =
(1 +1/√a)/√a(√a+1) =1/a . при a=3 1/3 ⇒В =0,3.
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* * * В= a^(-1/2) +( a^(-1/2) - a^(1/2) ) /(a+a^(1/2))
= ( a^(1/2) + 1+ a^(-1/2) - a^(1/2) ) /a^(1/2)*(a^(1/2)+1) =
( 1+ a^(-1/2) ) /a^(1/2)*(a^(1/2)+1) =( a^(1/2)+ 1 )/a(a^(1/2)+1) =1/a.