8u^2-22u+5 eching

$$8 u ^ { 2 } - 22 u + 5$$

Omil

$$\left(2u-5\right)\left(4u-1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 8u^{2}+au+bu+5 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-22 ab=8\times 5=40$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 40-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-40 -2,-20 -4,-10 -5,-8$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-40=-41 -2-20=-22 -4-10=-14 -5-8=-13$$

Yechim – -22 yigʻindisini beruvchi juftlik.

$$a=-20 b=-2$$

8u^{2}-22u+5 ni \left(8u^{2}-20u\right)+\left(-2u+5\right) sifatida qaytadan yozish.

$$\left(8u^{2}-20u\right)+\left(-2u+5\right)$$

Birinchi guruhda 4u ni va ikkinchi guruhda -1 ni faktordan chiqaring.

$$4u\left(2u-5\right)-\left(2u-5\right)$$

Distributiv funktsiyasidan foydalangan holda 2u-5 umumiy terminini chiqaring.

$$\left(2u-5\right)\left(4u-1\right)$$

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.

$$8u^{2}-22u+5=0$$

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.

$$u=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\times 8\times 5}}{2\times 8}$$

-22 kvadratini chiqarish.

$$u=\frac{-\left(-22\right)±\sqrt{484-4\times 8\times 5}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$u=\frac{-\left(-22\right)±\sqrt{484-32\times 5}}{2\times 8}$$

-32 ni 5 marotabaga ko'paytirish.

$$u=\frac{-\left(-22\right)±\sqrt{484-160}}{2\times 8}$$

484 ni -160 ga qo'shish.

$$u=\frac{-\left(-22\right)±\sqrt{324}}{2\times 8}$$

324 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-22\right)±18}{2\times 8}$$

-22 ning teskarisi 22 ga teng.

$$u=\frac{22±18}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$u=\frac{22±18}{16}$$

u=\frac{22±18}{16} tenglamasini yeching, bunda ± musbat. 22 ni 18 ga qo'shish.

$$u=\frac{40}{16}$$

\frac{40}{16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$u=\frac{5}{2}$$

u=\frac{22±18}{16} tenglamasini yeching, bunda ± manfiy. 22 dan 18 ni ayirish.

$$u=\frac{4}{16}$$

\frac{4}{16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$u=\frac{1}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5}{2} ga va x_{2} uchun \frac{1}{4} ga bo‘ling.

$$8u^{2}-22u+5=8\left(u-\frac{5}{2}\right)\left(u-\frac{1}{4}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{5}{2} ni u dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$8u^{2}-22u+5=8\times \frac{2u-5}{2}\left(u-\frac{1}{4}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{4} ni u dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$8u^{2}-22u+5=8\times \frac{2u-5}{2}\times \frac{4u-1}{4}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{2u-5}{2} ni \frac{4u-1}{4} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$8u^{2}-22u+5=8\times \frac{\left(2u-5\right)\left(4u-1\right)}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$8u^{2}-22u+5=8\times \frac{\left(2u-5\right)\left(4u-1\right)}{8}$$

8 va 8 ichida eng katta umumiy 8 faktorini bekor qiling.

$$8u^{2}-22u+5=\left(2u-5\right)\left(4u-1\right)$$

Baholash

$$\left(2u-5\right)\left(4u-1\right)$$