A(x)=x^5+x^2+x+2:B(x)=x^3-x+1 eching

$$A ( x ) = x ^ { 5 } + x ^ { 2 } + x + 2 : B ( x ) = x ^ { 3 } - x + 1$$

B uchun yechish

$$B=-\frac{2x}{x^{5}-x^{3}+x^{2}+2x-1}$$

$$x\neq 0\text{ and }x\left(x^{4}-x^{2}+x+2\right)\neq 1\text{ and }x^{5}-x^{3}+x^{2}+2x-1\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

B qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini B ga ko'paytirish.

$$Bx^{5}+Bx^{2}+Bx+2x=Bx^{3}-xB+B$$

Ikkala tarafdan Bx^{3} ni ayirish.

$$Bx^{5}+Bx^{2}+Bx+2x-Bx^{3}=-xB+B$$

xB ni ikki tarafga qo’shing.

$$Bx^{5}+Bx^{2}+Bx+2x-Bx^{3}+xB=B$$

Ikkala tarafdan B ni ayirish.

$$Bx^{5}+Bx^{2}+Bx+2x-Bx^{3}+xB-B=0$$

2Bx ni olish uchun Bx va xB ni birlashtirish.

$$Bx^{5}+Bx^{2}+2Bx+2x-Bx^{3}-B=0$$

Ikkala tarafdan 2x ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$Bx^{5}+Bx^{2}+2Bx-Bx^{3}-B=-2x$$

B'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{5}+x^{2}+2x-x^{3}-1\right)B=-2x$$

Tenglama standart shaklda.

$$\left(x^{5}-x^{3}+x^{2}+2x-1\right)B=-2x$$

Ikki tarafini x^{2}+x^{5}-1+2x-x^{3} ga bo‘ling.

$$\frac{\left(x^{5}-x^{3}+x^{2}+2x-1\right)B}{x^{5}-x^{3}+x^{2}+2x-1}=-\frac{2x}{x^{5}-x^{3}+x^{2}+2x-1}$$

x^{2}+x^{5}-1+2x-x^{3} ga bo'lish x^{2}+x^{5}-1+2x-x^{3} ga ko'paytirishni bekor qiladi.

$$B=-\frac{2x}{x^{5}-x^{3}+x^{2}+2x-1}$$

B qiymati 0 teng bo‘lmaydi.

$$B=-\frac{2x}{x^{5}-x^{3}+x^{2}+2x-1}\text{, }B\neq 0$$