Sigma(x-45)^2=3089 eching

$$\Sigma ( x - 45 ) ^ { 2 } = 3089$$

Σ uchun yechish

$$Σ=\frac{3089}{\left(x-45\right)^{2}}$$

$$x\neq 45$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-45\right)^{2} kengaytirilishi uchun ishlating.

$$Σ\left(x^{2}-90x+2025\right)=3089$$

Σ ga x^{2}-90x+2025 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Σx^{2}-90Σx+2025Σ=3089$$

Σ'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-90x+2025\right)Σ=3089$$

Ikki tarafini x^{2}-90x+2025 ga bo‘ling.

$$\frac{\left(x^{2}-90x+2025\right)Σ}{x^{2}-90x+2025}=\frac{3089}{x^{2}-90x+2025}$$

x^{2}-90x+2025 ga bo'lish x^{2}-90x+2025 ga ko'paytirishni bekor qiladi.

$$Σ=\frac{3089}{x^{2}-90x+2025}$$

3089 ni x^{2}-90x+2025 ga bo'lish.

$$Σ=\frac{3089}{\left(x-45\right)^{2}}$$

x uchun yechish (complex solution)

$$x=45+\sqrt{3089}Σ^{-\frac{1}{2}}$$

$$x=45-\sqrt{3089}Σ^{-\frac{1}{2}}\text{, }Σ\neq 0$$

x uchun yechish

$$x=45+\sqrt{\frac{3089}{Σ}}$$

$$x=45-\sqrt{\frac{3089}{Σ}}\text{, }Σ>0$$