lambda^2+75x-1900=0 eching

$$\lambda ^ { 2 } + 75 x - 1900 = 0$$

x uchun yechish

$$x=-\frac{\lambda ^{2}}{75}+\frac{76}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan \lambda ^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$75x-1900=-\lambda ^{2}$$

1900 ni ikki tarafga qo’shing.

$$75x=-\lambda ^{2}+1900$$

Tenglama standart shaklda.

$$75x=1900-\lambda ^{2}$$

Ikki tarafini 75 ga bo‘ling.

$$\frac{75x}{75}=\frac{1900-\lambda ^{2}}{75}$$

75 ga bo'lish 75 ga ko'paytirishni bekor qiladi.

$$x=\frac{1900-\lambda ^{2}}{75}$$

-\lambda ^{2}+1900 ni 75 ga bo'lish.

$$x=-\frac{\lambda ^{2}}{75}+\frac{76}{3}$$

λ uchun yechish (complex solution)

$$\lambda =-5\sqrt{76-3x}$$

$$\lambda =5\sqrt{76-3x}$$

λ uchun yechish

$$\lambda =5\sqrt{76-3x}$$

$$\lambda =-5\sqrt{76-3x}\text{, }x\leq \frac{76}{3}$$