z^2-3z+9/4=0 eching

$$z ^ { 2 } - 3 z + \frac { 9 } { 4 } = 0$$

z uchun yechish

$$z = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$z^{2}-3z+\frac{9}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va \frac{9}{4} ni c bilan almashtiring.

$$z=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times \frac{9}{4}}}{2}$$

-3 kvadratini chiqarish.

$$z=\frac{-\left(-3\right)±\sqrt{9-4\times \frac{9}{4}}}{2}$$

-4 ni \frac{9}{4} marotabaga ko'paytirish.

$$z=\frac{-\left(-3\right)±\sqrt{9-9}}{2}$$

9 ni -9 ga qo'shish.

$$z=\frac{-\left(-3\right)±\sqrt{0}}{2}$$

0 ning kvadrat ildizini chiqarish.

$$z=-\frac{-3}{2}$$

-3 ning teskarisi 3 ga teng.

$$z=\frac{3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$z^{2}-3z+\frac{9}{4}=0$$

z^{2}-3z+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(z-\frac{3}{2}\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(z-\frac{3}{2}\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$z-\frac{3}{2}=0 z-\frac{3}{2}=0$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$z=\frac{3}{2} z=\frac{3}{2}$$

Tenglama yechildi. Yechimlar bir xil.

$$z=\frac{3}{2}$$