2x^2+left(-xright)^2=180 eching

$$2 { x }^{ 2 } + { \left(-x \right) }^{ 2 } =180$$

x uchun yechish

$$x=2\sqrt{15}\approx 7,745966692$$

$$x=-2\sqrt{15}\approx -7,745966692$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini -x ga hisoblang va x^{2} ni qiymatni oling.

$$2x^{2}+x^{2}=180$$

3x^{2} ni olish uchun 2x^{2} va x^{2} ni birlashtirish.

$$3x^{2}=180$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{180}{3}$$

60 ni olish uchun 180 ni 3 ga bo‘ling.

$$x^{2}=60$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{15} x=-2\sqrt{15}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini -x ga hisoblang va x^{2} ni qiymatni oling.

$$2x^{2}+x^{2}=180$$

3x^{2} ni olish uchun 2x^{2} va x^{2} ni birlashtirish.

$$3x^{2}=180$$

Ikkala tarafdan 180 ni ayirish.

$$3x^{2}-180=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -180 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-180\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-180\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-180\right)}}{2\times 3}$$

-12 ni -180 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{2160}}{2\times 3}$$

2160 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{15}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{15}}{6}$$

x=\frac{0±12\sqrt{15}}{6} tenglamasini yeching, bunda ± musbat.

$$x=2\sqrt{15}$$

x=\frac{0±12\sqrt{15}}{6} tenglamasini yeching, bunda ± manfiy.

$$x=-2\sqrt{15}$$

Tenglama yechildi.

$$x=2\sqrt{15} x=-2\sqrt{15}$$