x^2+120^2=(5+x)^2 eching

$$x ^ { 2 } + 120 ^ { 2 } = ( 5 + x ) ^ { 2 }$$

x uchun yechish

$$x = \frac{2875}{2} = 1437\frac{1}{2} = 1437,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2 daraja ko‘rsatkichini 120 ga hisoblang va 14400 ni qiymatni oling.

$$x^{2}+14400=\left(5+x\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(5+x\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}+14400=25+10x+x^{2}$$

Ikkala tarafdan 10x ni ayirish.

$$x^{2}+14400-10x=25+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}+14400-10x-x^{2}=25$$

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

$$14400-10x=25$$

Ikkala tarafdan 14400 ni ayirish.

$$-10x=25-14400$$

-14375 olish uchun 25 dan 14400 ni ayirish.

$$-10x=-14375$$

Ikki tarafini -10 ga bo‘ling.

$$x=\frac{-14375}{-10}$$

\frac{-14375}{-10} ulushini -5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{2875}{2}$$