(3x)^2+(4x)^2=(5x)^2 eching

$$( 3 x ) ^ { 2 } + ( 4 x ) ^ { 2 } = ( 5 x ) ^ { 2 }$$

x uchun yechish (complex solution)

$$x\in \mathrm{C}$$

Yechim qadamlari

\left(3x\right)^{2} ni kengaytirish.

$$3^{2}x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

\left(4x\right)^{2} ni kengaytirish.

$$9x^{2}+4^{2}x^{2}=\left(5x\right)^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$9x^{2}+16x^{2}=\left(5x\right)^{2}$$

25x^{2} ni olish uchun 9x^{2} va 16x^{2} ni birlashtirish.

$$25x^{2}=\left(5x\right)^{2}$$

\left(5x\right)^{2} ni kengaytirish.

$$25x^{2}=5^{2}x^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$25x^{2}=25x^{2}$$

Ikkala tarafdan 25x^{2} ni ayirish.

$$25x^{2}-25x^{2}=0$$

0 ni olish uchun 25x^{2} va -25x^{2} ni birlashtirish.

$$0=0$$

0 va 0 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{C}$$

x uchun yechish

$$x\in \mathrm{R}$$

Yechim qadamlari

\left(3x\right)^{2} ni kengaytirish.

$$3^{2}x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9x^{2}+\left(4x\right)^{2}=\left(5x\right)^{2}$$

\left(4x\right)^{2} ni kengaytirish.

$$9x^{2}+4^{2}x^{2}=\left(5x\right)^{2}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$9x^{2}+16x^{2}=\left(5x\right)^{2}$$

25x^{2} ni olish uchun 9x^{2} va 16x^{2} ni birlashtirish.

$$25x^{2}=\left(5x\right)^{2}$$

\left(5x\right)^{2} ni kengaytirish.

$$25x^{2}=5^{2}x^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$25x^{2}=25x^{2}$$

Ikkala tarafdan 25x^{2} ni ayirish.

$$25x^{2}-25x^{2}=0$$

0 ni olish uchun 25x^{2} va -25x^{2} ni birlashtirish.

$$0=0$$

0 va 0 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{R}$$