-16t^2+64t-48 eching

$$- 16 t ^ { 2 } + 64 t - 48$$

Omil

$$16\left(1-t\right)\left(t-3\right)$$

Yechim qadamlari

16 omili.

$$16\left(-t^{2}+4t-3\right)$$

Hisoblang: -t^{2}+4t-3. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -t^{2}+at+bt-3 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=4 ab=-\left(-3\right)=3$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. Faqat bundan juftlik tizim yechimidir.

$$a=3 b=1$$

-t^{2}+4t-3 ni \left(-t^{2}+3t\right)+\left(t-3\right) sifatida qaytadan yozish.

$$\left(-t^{2}+3t\right)+\left(t-3\right)$$

-t^{2}+3t ichida -t ni ajrating.

$$-t\left(t-3\right)+t-3$$

Distributiv funktsiyasidan foydalangan holda t-3 umumiy terminini chiqaring.

$$\left(t-3\right)\left(-t+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$16\left(t-3\right)\left(-t+1\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$-16t^{2}+64t-48=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$t=\frac{-64±\sqrt{64^{2}-4\left(-16\right)\left(-48\right)}}{2\left(-16\right)}$$

64 kvadratini chiqarish.

$$t=\frac{-64±\sqrt{4096-4\left(-16\right)\left(-48\right)}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$t=\frac{-64±\sqrt{4096+64\left(-48\right)}}{2\left(-16\right)}$$

64 ni -48 marotabaga ko'paytirish.

$$t=\frac{-64±\sqrt{4096-3072}}{2\left(-16\right)}$$

4096 ni -3072 ga qo'shish.

$$t=\frac{-64±\sqrt{1024}}{2\left(-16\right)}$$

1024 ning kvadrat ildizini chiqarish.

$$t=\frac{-64±32}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$t=\frac{-64±32}{-32}$$

t=\frac{-64±32}{-32} tenglamasini yeching, bunda ± musbat. -64 ni 32 ga qo'shish.

$$t=-\frac{32}{-32}$$

-32 ni -32 ga bo'lish.

$$t=1$$

t=\frac{-64±32}{-32} tenglamasini yeching, bunda ± manfiy. -64 dan 32 ni ayirish.

$$t=-\frac{96}{-32}$$

-96 ni -32 ga bo'lish.

$$t=3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 1 ga va x_{2} uchun 3 ga bo‘ling.

$$-16t^{2}+64t-48=-16\left(t-1\right)\left(t-3\right)$$

Baholash

$$16\left(1-t\right)\left(t-3\right)$$