16x^2=49 eching

$$16 x ^ { 2 } = 49$$

x uchun yechish

$$x = \frac{7}{4} = 1\frac{3}{4} = 1,75$$

$$x = -\frac{7}{4} = -1\frac{3}{4} = -1,75$$

Kvadratlar farqidan foydalangan qadamlar

Ikki tarafini 16 ga bo‘ling.

$$x^{2}=\frac{49}{16}$$

Ikkala tarafdan \frac{49}{16} ni ayirish.

$$x^{2}-\frac{49}{16}=0$$

Ikkala tarafini 16 ga ko‘paytiring.

$$16x^{2}-49=0$$

Hisoblang: 16x^{2}-49. 16x^{2}-49 ni \left(4x\right)^{2}-7^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-7\right)\left(4x+7\right)=0$$

Tenglamani yechish uchun 4x-7=0 va 4x+7=0 ni yeching.

$$x=\frac{7}{4} x=-\frac{7}{4}$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikki tarafini 16 ga bo‘ling.

$$x^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{7}{4} x=-\frac{7}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 16 ga bo‘ling.

$$x^{2}=\frac{49}{16}$$

Ikkala tarafdan \frac{49}{16} ni ayirish.

$$x^{2}-\frac{49}{16}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -\frac{49}{16} ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{16}\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-\frac{49}{16}\right)}}{2}$$

-4 ni -\frac{49}{16} marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{\frac{49}{4}}}{2}$$

\frac{49}{4} ning kvadrat ildizini chiqarish.

$$x=\frac{0±\frac{7}{2}}{2}$$

x=\frac{0±\frac{7}{2}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\frac{7}{4}$$

x=\frac{0±\frac{7}{2}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{7}{4}$$

Tenglama yechildi.

$$x=\frac{7}{4} x=-\frac{7}{4}$$