$$ \left. \begin{array} { l } { x = \sqrt { 3 } - 2 } \ { y = \sqrt { 3 } - 1 } \end{array} ight\} \Rightarrow \sqrt[ 4 ] { x ^ { 4 } } + \sqrt { ( x - y ) ^ { 2 } } = ? $$

Question

$$ \left. \begin{array} { l } { x = \sqrt { 3 } - 2 } \ { y = \sqrt { 3 } - 1 } \end{array} ight\} \Rightarrow \sqrt[ 4 ] { x ^ { 4 } } + \sqrt { ( x - y ) ^ { 2 } } = ? $$

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Berilgan tenglamalar:

$$
\begin{array} { l } { x = \sqrt { 3 } - 2 } \ { y = \sqrt { 3 } - 1 } \end{array}
$$

Bizga quyidagi ifodani hisoblash kerak:

$$
\sqrt[4]{x^4} + \sqrt{(x - y)^2}
$$

1. **Birinchi qadam:** $$ \sqrt[4]{x^4} $$ ni hisoblaymiz. Bu ifoda $$ |x| $$ ga teng, chunki $$ \sqrt[4]{x^4} = |x| $$.

2. **Ikkinchi qadam:** $$ x $$ ni hisoblaymiz:
   $$
   x = \sqrt{3} - 2
   $$
   $$ \sqrt{3} $$ taxminan 1.732 ga teng, shuning uchun:
   $$
   x \approx 1.732 - 2 = -0.268
   $$
   Demak, $$ |x| = -x = 2 - \sqrt{3} $$.

3. **Uchinchi qadam:** $$ y $$ ni hisoblaymiz:
   $$
   y = \sqrt{3} - 1 \approx 1.732 - 1 = 0.732
   $$

4. **To'rtinchi qadam:** $$ x - y $$ ni hisoblaymiz:
   $$
   x - y = (\sqrt{3} - 2) - (\sqrt{3} - 1) = -2 + 1 = -1
   $$
   Shunday qilib, $$ (x - y)^2 = (-1)^2 = 1 $$.

5. **Beshinchi qadam:** Endi ifodani to'liq hisoblaymiz:
   $$
   \sqrt[4]{x^4} + \sqrt{(x - y)^2} = |x| + \sqrt{1} = (2 - \sqrt{3}) + 1
   $$

6. **Oltinchi qadam:** Natijani hisoblaymiz:
   $$
   2 - \sqrt{3} + 1 = 3 - \sqrt{3}
   $$

Shunday qilib, natija:

$$
\sqrt[4]{x^4} + \sqrt{(x - y)^2} = 3 - \sqrt{3}
$$
Natija: $$ 3 - \sqrt{3} $$.

\( \left. \begin{array} { l } { x = \sqrt { 3 } - 2 } \\ { y = \sqrt { 3 } - 1 } \end{array} \right\} \Rightarrow \sqrt[ 4 ] { x ^ { 4 } } + \sqrt { ( x - y ) ^ { 2 } } = ? \)

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