m^2+9<(1-m)^2 eching

$$m ^ { 2 } + 9 < ( 1 - m ) ^ { 2 }$$

m uchun yechish

$$m<-4$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(1-m\right)^{2} kengaytirilishi uchun ishlating.

$$m^{2}+9<1-2m+m^{2}$$

2m ni ikki tarafga qo’shing.

$$m^{2}+9+2m<1+m^{2}$$

Ikkala tarafdan m^{2} ni ayirish.

$$m^{2}+9+2m-m^{2}<1$$

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

$$9+2m<1$$

Ikkala tarafdan 9 ni ayirish.

$$2m<1-9$$

-8 olish uchun 1 dan 9 ni ayirish.

$$2m<-8$$

Ikki tarafini 2 ga bo‘ling. 2 musbat bo‘lgani uchun, tengsizlik yo‘nalishi o‘zgarmaydi.

$$m<\frac{-8}{2}$$

-4 ni olish uchun -8 ni 2 ga bo‘ling.

$$m<-4$$