x^2/4=x^2/9+1/9 eching

$$\frac { x ^ { 2 } } { 4 } = \frac { x ^ { 2 } } { 9 } + \frac { 1 } { 9 }$$

x uchun yechish

$$x=\frac{2\sqrt{5}}{5}\approx 0,894427191$$

$$x=-\frac{2\sqrt{5}}{5}\approx -0,894427191$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 36 ga, 4,9 ning eng kichik karralisiga ko‘paytiring.

$$9x^{2}=4x^{2}+4$$

Ikkala tarafdan 4x^{2} ni ayirish.

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

5x^{2} ni olish uchun 9x^{2} va -4x^{2} ni birlashtirish.

$$5x^{2}=4$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}=\frac{4}{5}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 36 ga, 4,9 ning eng kichik karralisiga ko‘paytiring.

$$9x^{2}=4x^{2}+4$$

Ikkala tarafdan 4x^{2} ni ayirish.

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

5x^{2} ni olish uchun 9x^{2} va -4x^{2} ni birlashtirish.

$$5x^{2}=4$$

Ikkala tarafdan 4 ni ayirish.

$$5x^{2}-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, 0 ni b va -4 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-4\right)}}{2\times 5}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 5\left(-4\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-20\left(-4\right)}}{2\times 5}$$

-20 ni -4 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{80}}{2\times 5}$$

80 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{5}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{5}}{10}$$

x=\frac{0±4\sqrt{5}}{10} tenglamasini yeching, bunda ± musbat.

$$x=\frac{2\sqrt{5}}{5}$$

x=\frac{0±4\sqrt{5}}{10} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{2\sqrt{5}}{5}$$

Tenglama yechildi.

$$x=\frac{2\sqrt{5}}{5} x=-\frac{2\sqrt{5}}{5}$$