sqrt{left(12+xright)^2-x^2}=16*16 eching

$$\sqrt{ { \left(12+x \right) }^{ 2 } - { x }^{ 2 } } =16 \times 16$$

x uchun yechish

$$x = \frac{8174}{3} = 2724\frac{2}{3} \approx 2724,666666667$$

Ildizli tenglamalarni yechish qadamlari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(12+x\right)^{2} kengaytirilishi uchun ishlating.

$$\sqrt{144+24x+x^{2}-x^{2}}=16\times 16$$

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

$$\sqrt{144+24x}=16\times 16$$

256 hosil qilish uchun 16 va 16 ni ko'paytirish.

$$\sqrt{144+24x}=256$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$24x+144=65536$$

Tenglamaning ikkala tarafidan 144 ni ayirish.

$$24x+144-144=65536-144$$

O‘zidan 144 ayirilsa 0 qoladi.

$$24x=65536-144$$

65536 dan 144 ni ayirish.

$$24x=65392$$

Ikki tarafini 24 ga bo‘ling.

$$\frac{24x}{24}=\frac{65392}{24}$$

24 ga bo'lish 24 ga ko'paytirishni bekor qiladi.

$$x=\frac{65392}{24}$$

\frac{65392}{24} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{8174}{3}$$