49x^2+63x+18 eching

$$49 x ^ { 2 } + 63 x + 18$$

Omil

$$\left(7x+3\right)\left(7x+6\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 49x^{2}+ax+bx+18 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=63 ab=49\times 18=882$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 882-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,882 2,441 3,294 6,147 7,126 9,98 14,63 18,49 21,42$$

Har bir juftlik yigʻindisini hisoblang.

$$1+882=883 2+441=443 3+294=297 6+147=153 7+126=133 9+98=107 14+63=77 18+49=67 21+42=63$$

Yechim – 63 yigʻindisini beruvchi juftlik.

$$a=21 b=42$$

49x^{2}+63x+18 ni \left(49x^{2}+21x\right)+\left(42x+18\right) sifatida qaytadan yozish.

$$\left(49x^{2}+21x\right)+\left(42x+18\right)$$

Birinchi guruhda 7x ni va ikkinchi guruhda 6 ni faktordan chiqaring.

$$7x\left(7x+3\right)+6\left(7x+3\right)$$

Distributiv funktsiyasidan foydalangan holda 7x+3 umumiy terminini chiqaring.

$$\left(7x+3\right)\left(7x+6\right)$$

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.

$$49x^{2}+63x+18=0$$

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.

$$x=\frac{-63±\sqrt{63^{2}-4\times 49\times 18}}{2\times 49}$$

63 kvadratini chiqarish.

$$x=\frac{-63±\sqrt{3969-4\times 49\times 18}}{2\times 49}$$

-4 ni 49 marotabaga ko'paytirish.

$$x=\frac{-63±\sqrt{3969-196\times 18}}{2\times 49}$$

-196 ni 18 marotabaga ko'paytirish.

$$x=\frac{-63±\sqrt{3969-3528}}{2\times 49}$$

3969 ni -3528 ga qo'shish.

$$x=\frac{-63±\sqrt{441}}{2\times 49}$$

441 ning kvadrat ildizini chiqarish.

$$x=\frac{-63±21}{2\times 49}$$

2 ni 49 marotabaga ko'paytirish.

$$x=\frac{-63±21}{98}$$

x=\frac{-63±21}{98} tenglamasini yeching, bunda ± musbat. -63 ni 21 ga qo'shish.

$$x=-\frac{42}{98}$$

\frac{-42}{98} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{3}{7}$$

x=\frac{-63±21}{98} tenglamasini yeching, bunda ± manfiy. -63 dan 21 ni ayirish.

$$x=-\frac{84}{98}$$

\frac{-84}{98} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{6}{7}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{3}{7} ga va x_{2} uchun -\frac{6}{7} ga bo‘ling.

$$49x^{2}+63x+18=49\left(x-\left(-\frac{3}{7}\right)\right)\left(x-\left(-\frac{6}{7}\right)\right)$$

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

$$49x^{2}+63x+18=49\left(x+\frac{3}{7}\right)\left(x+\frac{6}{7}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{7} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$49x^{2}+63x+18=49\times \frac{7x+3}{7}\left(x+\frac{6}{7}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{6}{7} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$49x^{2}+63x+18=49\times \frac{7x+3}{7}\times \frac{7x+6}{7}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{7x+3}{7} ni \frac{7x+6}{7} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$49x^{2}+63x+18=49\times \frac{\left(7x+3\right)\left(7x+6\right)}{7\times 7}$$

7 ni 7 marotabaga ko'paytirish.

$$49x^{2}+63x+18=49\times \frac{\left(7x+3\right)\left(7x+6\right)}{49}$$

49 va 49 ichida eng katta umumiy 49 faktorini bekor qiling.

$$49x^{2}+63x+18=\left(7x+3\right)\left(7x+6\right)$$

Baholash

$$\left(7x+3\right)\left(7x+6\right)$$