x/3*3+x/4*4+x/6*5+(x/4-8)*2=50^4 eching

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } \times 5 + ( \frac { x } { 4 } - 8 ) \cdot 2 = 50 ^ { 4 }$$

x uchun yechish

$$x = \frac{9375024}{5} = 1875004\frac{4}{5} = 1875004,8$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini 12 ga, 3,4,6 ning eng kichik karralisiga ko‘paytiring.

$$4x\times 3+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$12x+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$12x+12x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

24x ni olish uchun 12x va 12x ni birlashtirish.

$$24x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$24x+10x+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

34x ni olish uchun 24x va 10x ni birlashtirish.

$$34x+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

24 hosil qilish uchun 12 va 2 ni ko'paytirish.

$$34x+24\left(\frac{x}{4}-8\right)=12\times 50^{4}$$

24 ga \frac{x}{4}-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$34x+24\times \frac{x}{4}-192=12\times 50^{4}$$

24 va 4 ichida eng katta umumiy 4 faktorini bekor qiling.

$$34x+6x-192=12\times 50^{4}$$

40x ni olish uchun 34x va 6x ni birlashtirish.

$$40x-192=12\times 50^{4}$$

4 daraja ko‘rsatkichini 50 ga hisoblang va 6250000 ni qiymatni oling.

$$40x-192=12\times 6250000$$

75000000 hosil qilish uchun 12 va 6250000 ni ko'paytirish.

$$40x-192=75000000$$

192 ni ikki tarafga qo’shing.

$$40x=75000000+192$$

75000192 olish uchun 75000000 va 192'ni qo'shing.

$$40x=75000192$$

Ikki tarafini 40 ga bo‘ling.

$$x=\frac{75000192}{40}$$

\frac{75000192}{40} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{9375024}{5}$$