2u^2-34u+60 eching

$$2 u ^ { 2 } - 34 u + 60$$

Omil

$$2\left(u-15\right)\left(u-2\right)$$

Yechim qadamlari

2 omili.

$$2\left(u^{2}-17u+30\right)$$

Hisoblang: u^{2}-17u+30. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda u^{2}+au+bu+30 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-17 ab=1\times 30=30$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 30-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-30 -2,-15 -3,-10 -5,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

Yechim – -17 yigʻindisini beruvchi juftlik.

$$a=-15 b=-2$$

u^{2}-17u+30 ni \left(u^{2}-15u\right)+\left(-2u+30\right) sifatida qaytadan yozish.

$$\left(u^{2}-15u\right)+\left(-2u+30\right)$$

Birinchi guruhda u ni va ikkinchi guruhda -2 ni faktordan chiqaring.

$$u\left(u-15\right)-2\left(u-15\right)$$

Distributiv funktsiyasidan foydalangan holda u-15 umumiy terminini chiqaring.

$$\left(u-15\right)\left(u-2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$2\left(u-15\right)\left(u-2\right)$$

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.

$$2u^{2}-34u+60=0$$

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.

$$u=\frac{-\left(-34\right)±\sqrt{\left(-34\right)^{2}-4\times 2\times 60}}{2\times 2}$$

-34 kvadratini chiqarish.

$$u=\frac{-\left(-34\right)±\sqrt{1156-4\times 2\times 60}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$u=\frac{-\left(-34\right)±\sqrt{1156-8\times 60}}{2\times 2}$$

-8 ni 60 marotabaga ko'paytirish.

$$u=\frac{-\left(-34\right)±\sqrt{1156-480}}{2\times 2}$$

1156 ni -480 ga qo'shish.

$$u=\frac{-\left(-34\right)±\sqrt{676}}{2\times 2}$$

676 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-34\right)±26}{2\times 2}$$

-34 ning teskarisi 34 ga teng.

$$u=\frac{34±26}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$u=\frac{34±26}{4}$$

u=\frac{34±26}{4} tenglamasini yeching, bunda ± musbat. 34 ni 26 ga qo'shish.

$$u=\frac{60}{4}$$

60 ni 4 ga bo'lish.

$$u=15$$

u=\frac{34±26}{4} tenglamasini yeching, bunda ± manfiy. 34 dan 26 ni ayirish.

$$u=\frac{8}{4}$$

8 ni 4 ga bo'lish.

$$u=2$$

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 2 ga bo‘ling.

$$2u^{2}-34u+60=2\left(u-15\right)\left(u-2\right)$$

Baholash

$$2\left(u-15\right)\left(u-2\right)$$