72x^2+67=99 eching

$$72 { x }^{ 2 } +67=99$$

x uchun yechish

$$x=\frac{2}{3}\approx 0,666666667$$

$$x=-\frac{2}{3}\approx -0,666666667$$

Kvadratlar farqidan foydalangan qadamlar

Ikkala tarafdan 99 ni ayirish.

$$72x^{2}+67-99=0$$

-32 olish uchun 67 dan 99 ni ayirish.

$$72x^{2}-32=0$$

Ikki tarafini 8 ga bo‘ling.

$$9x^{2}-4=0$$

Hisoblang: 9x^{2}-4. 9x^{2}-4 ni \left(3x\right)^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-2\right)\left(3x+2\right)=0$$

Tenglamani yechish uchun 3x-2=0 va 3x+2=0 ni yeching.

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

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 67 ni ayirish.

$$72x^{2}=99-67$$

32 olish uchun 99 dan 67 ni ayirish.

$$72x^{2}=32$$

Ikki tarafini 72 ga bo‘ling.

$$x^{2}=\frac{32}{72}$$

\frac{32}{72} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{4}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 99 ni ayirish.

$$72x^{2}+67-99=0$$

-32 olish uchun 67 dan 99 ni ayirish.

$$72x^{2}-32=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 72 ni a, 0 ni b va -32 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 72\left(-32\right)}}{2\times 72}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 72\left(-32\right)}}{2\times 72}$$

-4 ni 72 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-288\left(-32\right)}}{2\times 72}$$

-288 ni -32 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{9216}}{2\times 72}$$

9216 ning kvadrat ildizini chiqarish.

$$x=\frac{0±96}{2\times 72}$$

2 ni 72 marotabaga ko'paytirish.

$$x=\frac{0±96}{144}$$

x=\frac{0±96}{144} tenglamasini yeching, bunda ± musbat. \frac{96}{144} ulushini 48 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{0±96}{144} tenglamasini yeching, bunda ± manfiy. \frac{-96}{144} ulushini 48 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Tenglama yechildi.

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