1/2+sqrt{3}+|sin30^circ-1| eching

$$\frac { 1 } { 2 + \sqrt { 3 } } + | \sin 30 ^ { \circ } - 1 |$$

Baholash

$$\frac{5}{2}-\sqrt{3}\approx 0,767949192$$

Yechim qadamlari

\frac{1}{2+\sqrt{3}} maxrajini 2-\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+|\sin(30)-1|$$

Hisoblang: \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2-\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}+|\sin(30)-1|$$

2 kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

$$\frac{2-\sqrt{3}}{4-3}+|\sin(30)-1|$$

1 olish uchun 4 dan 3 ni ayirish.

$$\frac{2-\sqrt{3}}{1}+|\sin(30)-1|$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$2-\sqrt{3}+|\sin(30)-1|$$

Trigonometrik qiymatlar jadvaldan \sin(30) qiymatini oling.

$$2-\sqrt{3}+|\frac{1}{2}-1|$$

-\frac{1}{2} olish uchun \frac{1}{2} dan 1 ni ayirish.

$$2-\sqrt{3}+|-\frac{1}{2}|$$

a haqiqiy sonining mutloq qiymati qachon a\geq 0 bo‘lganda, a yoki qachon a<0 bo‘lganda -a. -\frac{1}{2} ning mutloq qiymati \frac{1}{2} ga teng.

$$2-\sqrt{3}+\frac{1}{2}$$

\frac{5}{2} olish uchun 2 va \frac{1}{2}'ni qo'shing.

$$\frac{5}{2}-\sqrt{3}$$