-3u^2-36u+135 eching

$$- 3 u ^ { 2 } - 36 u + 135$$

Omil

$$3\left(3-u\right)\left(u+15\right)$$

Yechim qadamlari

3 omili.

$$3\left(-u^{2}-12u+45\right)$$

Hisoblang: -u^{2}-12u+45. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -u^{2}+au+bu+45 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-12 ab=-45=-45$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -45-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-45 3,-15 5,-9$$

Har bir juftlik yigʻindisini hisoblang.

$$1-45=-44 3-15=-12 5-9=-4$$

Yechim – -12 yigʻindisini beruvchi juftlik.

$$a=3 b=-15$$

-u^{2}-12u+45 ni \left(-u^{2}+3u\right)+\left(-15u+45\right) sifatida qaytadan yozish.

$$\left(-u^{2}+3u\right)+\left(-15u+45\right)$$

Birinchi guruhda u ni va ikkinchi guruhda 15 ni faktordan chiqaring.

$$u\left(-u+3\right)+15\left(-u+3\right)$$

Distributiv funktsiyasidan foydalangan holda -u+3 umumiy terminini chiqaring.

$$\left(-u+3\right)\left(u+15\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3\left(-u+3\right)\left(u+15\right)$$

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.

$$-3u^{2}-36u+135=0$$

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.

$$u=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\left(-3\right)\times 135}}{2\left(-3\right)}$$

-36 kvadratini chiqarish.

$$u=\frac{-\left(-36\right)±\sqrt{1296-4\left(-3\right)\times 135}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$u=\frac{-\left(-36\right)±\sqrt{1296+12\times 135}}{2\left(-3\right)}$$

12 ni 135 marotabaga ko'paytirish.

$$u=\frac{-\left(-36\right)±\sqrt{1296+1620}}{2\left(-3\right)}$$

1296 ni 1620 ga qo'shish.

$$u=\frac{-\left(-36\right)±\sqrt{2916}}{2\left(-3\right)}$$

2916 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-36\right)±54}{2\left(-3\right)}$$

-36 ning teskarisi 36 ga teng.

$$u=\frac{36±54}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$u=\frac{36±54}{-6}$$

u=\frac{36±54}{-6} tenglamasini yeching, bunda ± musbat. 36 ni 54 ga qo'shish.

$$u=\frac{90}{-6}$$

90 ni -6 ga bo'lish.

$$u=-15$$

u=\frac{36±54}{-6} tenglamasini yeching, bunda ± manfiy. 36 dan 54 ni ayirish.

$$u=-\frac{18}{-6}$$

-18 ni -6 ga bo'lish.

$$u=3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -15 ga va x_{2} uchun 3 ga bo‘ling.

$$-3u^{2}-36u+135=-3\left(u-\left(-15\right)\right)\left(u-3\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$-3u^{2}-36u+135=-3\left(u+15\right)\left(u-3\right)$$

Baholash

$$3\left(3-u\right)\left(u+15\right)$$