(a+b)^2-4ab=(a-b)^2 eching

$$( a + b ) ^ { 2 } - 4 a b = ( a - b ) ^ { 2 }$$

a uchun yechish (complex solution)

$$a\in \mathrm{C}$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a+b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+2ab+b^{2}-4ab=\left(a-b\right)^{2}$$

-2ab ni olish uchun 2ab va -4ab ni birlashtirish.

$$a^{2}-2ab+b^{2}=\left(a-b\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}-2ab+b^{2}=a^{2}-2ab+b^{2}$$

Ikkala tarafdan a^{2} ni ayirish.

$$a^{2}-2ab+b^{2}-a^{2}=-2ab+b^{2}$$

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

$$-2ab+b^{2}=-2ab+b^{2}$$

2ab ni ikki tarafga qo’shing.

$$-2ab+b^{2}+2ab=b^{2}$$

0 ni olish uchun -2ab va 2ab ni birlashtirish.

$$b^{2}=b^{2}$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday a uchun to‘g‘ri.

$$a\in \mathrm{C}$$

b uchun yechish (complex solution)

$$b\in \mathrm{C}$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a+b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+2ab+b^{2}-4ab=\left(a-b\right)^{2}$$

-2ab ni olish uchun 2ab va -4ab ni birlashtirish.

$$a^{2}-2ab+b^{2}=\left(a-b\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}-2ab+b^{2}=a^{2}-2ab+b^{2}$$

2ab ni ikki tarafga qo’shing.

$$a^{2}-2ab+b^{2}+2ab=a^{2}+b^{2}$$

0 ni olish uchun -2ab va 2ab ni birlashtirish.

$$a^{2}+b^{2}=a^{2}+b^{2}$$

Ikkala tarafdan b^{2} ni ayirish.

$$a^{2}+b^{2}-b^{2}=a^{2}$$

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

$$a^{2}=a^{2}$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday b uchun to‘g‘ri.

$$b\in \mathrm{C}$$

a uchun yechish

$$a\in \mathrm{R}$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a+b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+2ab+b^{2}-4ab=\left(a-b\right)^{2}$$

-2ab ni olish uchun 2ab va -4ab ni birlashtirish.

$$a^{2}-2ab+b^{2}=\left(a-b\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}-2ab+b^{2}=a^{2}-2ab+b^{2}$$

Ikkala tarafdan a^{2} ni ayirish.

$$a^{2}-2ab+b^{2}-a^{2}=-2ab+b^{2}$$

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

$$-2ab+b^{2}=-2ab+b^{2}$$

2ab ni ikki tarafga qo’shing.

$$-2ab+b^{2}+2ab=b^{2}$$

0 ni olish uchun -2ab va 2ab ni birlashtirish.

$$b^{2}=b^{2}$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday a uchun to‘g‘ri.

$$a\in \mathrm{R}$$

b uchun yechish

$$b\in \mathrm{R}$$

Yechim qadamlari

\left(p+q\right)^{2}=p^{2}+2pq+q^{2} binom teoremasini \left(a+b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}+2ab+b^{2}-4ab=\left(a-b\right)^{2}$$

-2ab ni olish uchun 2ab va -4ab ni birlashtirish.

$$a^{2}-2ab+b^{2}=\left(a-b\right)^{2}$$

\left(p-q\right)^{2}=p^{2}-2pq+q^{2} binom teoremasini \left(a-b\right)^{2} kengaytirilishi uchun ishlating.

$$a^{2}-2ab+b^{2}=a^{2}-2ab+b^{2}$$

2ab ni ikki tarafga qo’shing.

$$a^{2}-2ab+b^{2}+2ab=a^{2}+b^{2}$$

0 ni olish uchun -2ab va 2ab ni birlashtirish.

$$a^{2}+b^{2}=a^{2}+b^{2}$$

Ikkala tarafdan b^{2} ni ayirish.

$$a^{2}+b^{2}-b^{2}=a^{2}$$

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

$$a^{2}=a^{2}$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday b uchun to‘g‘ri.

$$b\in \mathrm{R}$$