10^2-x^2=8^2-left(12-xright)^2 eching

$${ 10 }^{ 2 } - { x }^{ 2 } = { 8 }^{ 2 } - { \left(12-x \right) }^{ 2 }$$

x uchun yechish

$$x = \frac{15}{2} = 7\frac{1}{2} = 7,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2 daraja ko‘rsatkichini 10 ga hisoblang va 100 ni qiymatni oling.

$$100-x^{2}=8^{2}-\left(12-x\right)^{2}$$

2 daraja ko‘rsatkichini 8 ga hisoblang va 64 ni qiymatni oling.

$$100-x^{2}=64-\left(12-x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(12-x\right)^{2} kengaytirilishi uchun ishlating.

$$100-x^{2}=64-\left(144-24x+x^{2}\right)$$

144-24x+x^{2} teskarisini topish uchun har birining teskarisini toping.

$$100-x^{2}=64-144+24x-x^{2}$$

-80 olish uchun 64 dan 144 ni ayirish.

$$100-x^{2}=-80+24x-x^{2}$$

Ikkala tarafdan 24x ni ayirish.

$$100-x^{2}-24x=-80-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$100-x^{2}-24x+x^{2}=-80$$

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

$$100-24x=-80$$

Ikkala tarafdan 100 ni ayirish.

$$-24x=-80-100$$

-180 olish uchun -80 dan 100 ni ayirish.

$$-24x=-180$$

Ikki tarafini -24 ga bo‘ling.

$$x=\frac{-180}{-24}$$

\frac{-180}{-24} ulushini -12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{15}{2}$$