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18.03.2013

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11 + 218 + |218 - 11|.

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:

11 + 218 + |218 - 11| = x;

(11 + 218 + |218 - 11|)2 = x2;

11 + 2√18 + 2(11 + 218)(|218 - 11|) + |2√18 - 11| = x2;

2√18 11.

72 < 121, √72 < √121, 2√18 < 11. "-".

11 + 2√18 + 2121 - 72 + 11 - 2√18 = x2;

22 + 249 = x2;

22 + 14 = x2;

x = 6 (.. ).

: 6.


|125 - 29| - 125 + 29.

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12√5 29, .

720 < 841, √720 < √841 12√5 < 29. "-".

:

29 - 125 - 29 + 125 = x;

(29 - 125 - 29 + 125)2 = x2;

29 - 12√5 - 2(29 - 125)(29 + 125) + 29 + 12√5 = x2;

58 - 2√841 - 720 = x2;

36 = x2;

x = -6 (.. ).

: -6.


32 + 5 + 32 - 5.

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:

32 + 5 + 32 - 5 = x; (*)

(32 + 5 + 32 - 5)3 = x3;

2 + √5 + 3(3(2 + 5)(2 - 5)(32 + 5 + 32 - 5) + 2 - √5 = x3;

(*) :

4 + 3x34 - 5 = x3;

x3 + 3x - 4 = 0;

x3 - x2 + x2 + 3x - 4 = 0;

x2(x - 1) + (x - 1)(x + 4) = 0;

(x - 1)(x2 + x + 4) = 0;

, x = 1. .

: 1.


320 + 142 + 320 - 142.

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:

320 + 142 + 320 - 142 = x; (*)

(320 + 142 + 320 - 142)3 = x3;

20 + 14√2 + 33(20 + 142)(20 - 142) (320 + 142 + 320 - 142) + 20 - 14√2 = x3;

(*) :

40 + 3x3400 - 392 = x3;

x3 - 6x - 40 = 0;

x3 - 16x + 10x - 40 = 0;

x(x2 - 16) + 10(x - 4) = 0;

x(x - 4)(x + 4) + 10(x - 4) = 0;

(x - 4)(x2 + 4x + 10) = 0;

, x = 4. .

: 4.


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