k^2-24k-48 eching

$$k ^ { 2 } - 24 k - 48$$

Omil

$$\left(k-\left(12-8\sqrt{3}\right)\right)\left(k-\left(8\sqrt{3}+12\right)\right)$$

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.

$$k^{2}-24k-48=0$$

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.

$$k=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\left(-48\right)}}{2}$$

-24 kvadratini chiqarish.

$$k=\frac{-\left(-24\right)±\sqrt{576-4\left(-48\right)}}{2}$$

-4 ni -48 marotabaga ko'paytirish.

$$k=\frac{-\left(-24\right)±\sqrt{576+192}}{2}$$

576 ni 192 ga qo'shish.

$$k=\frac{-\left(-24\right)±\sqrt{768}}{2}$$

768 ning kvadrat ildizini chiqarish.

$$k=\frac{-\left(-24\right)±16\sqrt{3}}{2}$$

-24 ning teskarisi 24 ga teng.

$$k=\frac{24±16\sqrt{3}}{2}$$

k=\frac{24±16\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat. 24 ni 16\sqrt{3} ga qo'shish.

$$k=\frac{16\sqrt{3}+24}{2}$$

24+16\sqrt{3} ni 2 ga bo'lish.

$$k=8\sqrt{3}+12$$

k=\frac{24±16\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy. 24 dan 16\sqrt{3} ni ayirish.

$$k=\frac{24-16\sqrt{3}}{2}$$

24-16\sqrt{3} ni 2 ga bo'lish.

$$k=12-8\sqrt{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 12+8\sqrt{3} ga va x_{2} uchun 12-8\sqrt{3} ga bo‘ling.

$$k^{2}-24k-48=\left(k-\left(8\sqrt{3}+12\right)\right)\left(k-\left(12-8\sqrt{3}\right)\right)$$

Baholash

$$k^{2}-24k-48$$