(2x+y-8)^2=(2x+y)^2+quad4y^4 eching

$$( 2 x + y - 8 ) ^ { 2 } = ( 2 x + y ) ^ { 2 } + \quad 4 y ^ { 4 }$$

x uchun yechish

$$x=-\frac{y^{4}}{8}-\frac{y}{2}+2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2x+y-8 kvadratini chiqarish.

$$4x^{2}+4xy-32x+y^{2}-16y+64=\left(2x+y\right)^{2}+4y^{4}$$

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

$$4x^{2}+4xy-32x+y^{2}-16y+64=4x^{2}+4xy+y^{2}+4y^{4}$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$4x^{2}+4xy-32x+y^{2}-16y+64-4x^{2}=4xy+y^{2}+4y^{4}$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$4xy-32x+y^{2}-16y+64=4xy+y^{2}+4y^{4}$$

Ikkala tarafdan 4xy ni ayirish.

$$4xy-32x+y^{2}-16y+64-4xy=y^{2}+4y^{4}$$

0 ni olish uchun 4xy va -4xy ni birlashtirish.

$$-32x+y^{2}-16y+64=y^{2}+4y^{4}$$

Ikkala tarafdan y^{2} ni ayirish.

$$-32x-16y+64=y^{2}+4y^{4}-y^{2}$$

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

$$-32x-16y+64=4y^{4}$$

16y ni ikki tarafga qo’shing.

$$-32x+64=4y^{4}+16y$$

Ikkala tarafdan 64 ni ayirish.

$$-32x=4y^{4}+16y-64$$

Ikki tarafini -32 ga bo‘ling.

$$\frac{-32x}{-32}=\frac{4y^{4}+16y-64}{-32}$$

-32 ga bo'lish -32 ga ko'paytirishni bekor qiladi.

$$x=\frac{4y^{4}+16y-64}{-32}$$

4y^{4}+16y-64 ni -32 ga bo'lish.

$$x=-\frac{y^{4}}{8}-\frac{y}{2}+2$$