18+21d-8d^2 eching

$$18 + 21 d - 8 d ^ { 2 }$$

Omil

$$-8\left(d-\frac{21-3\sqrt{113}}{16}\right)\left(d-\frac{3\sqrt{113}+21}{16}\right)$$

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.

$$-8d^{2}+21d+18=0$$

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.

$$d=\frac{-21±\sqrt{21^{2}-4\left(-8\right)\times 18}}{2\left(-8\right)}$$

21 kvadratini chiqarish.

$$d=\frac{-21±\sqrt{441-4\left(-8\right)\times 18}}{2\left(-8\right)}$$

-4 ni -8 marotabaga ko'paytirish.

$$d=\frac{-21±\sqrt{441+32\times 18}}{2\left(-8\right)}$$

32 ni 18 marotabaga ko'paytirish.

$$d=\frac{-21±\sqrt{441+576}}{2\left(-8\right)}$$

441 ni 576 ga qo'shish.

$$d=\frac{-21±\sqrt{1017}}{2\left(-8\right)}$$

1017 ning kvadrat ildizini chiqarish.

$$d=\frac{-21±3\sqrt{113}}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$d=\frac{-21±3\sqrt{113}}{-16}$$

d=\frac{-21±3\sqrt{113}}{-16} tenglamasini yeching, bunda ± musbat. -21 ni 3\sqrt{113} ga qo'shish.

$$d=\frac{3\sqrt{113}-21}{-16}$$

-21+3\sqrt{113} ni -16 ga bo'lish.

$$d=\frac{21-3\sqrt{113}}{16}$$

d=\frac{-21±3\sqrt{113}}{-16} tenglamasini yeching, bunda ± manfiy. -21 dan 3\sqrt{113} ni ayirish.

$$d=\frac{-3\sqrt{113}-21}{-16}$$

-21-3\sqrt{113} ni -16 ga bo'lish.

$$d=\frac{3\sqrt{113}+21}{16}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{21-3\sqrt{113}}{16} ga va x_{2} uchun \frac{21+3\sqrt{113}}{16} ga bo‘ling.

$$-8d^{2}+21d+18=-8\left(d-\frac{21-3\sqrt{113}}{16}\right)\left(d-\frac{3\sqrt{113}+21}{16}\right)$$

Baholash

$$18+21d-8d^{2}$$