x^2/4=x^2/9+5/9 eching

$$\frac { x ^ { 2 } } { 4 } = \frac { x ^ { 2 } } { 9 } + \frac { 5 } { 9 }$$

x uchun yechish

$$x=2$$

$$x=-2$$

Kvadratlar farqidan foydalangan qadamlar

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

$$9x^{2}=4x^{2}+20$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$9x^{2}-4x^{2}=20$$

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

$$5x^{2}=20$$

Ikkala tarafdan 20 ni ayirish.

$$5x^{2}-20=0$$

Ikki tarafini 5 ga bo‘ling.

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

Hisoblang: x^{2}-4. x^{2}-4 ni x^{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).

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

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

$$x=2 x=-2$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$9x^{2}=4x^{2}+20$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$9x^{2}-4x^{2}=20$$

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

$$5x^{2}=20$$

Ikki tarafini 5 ga bo‘ling.

$$x^{2}=\frac{20}{5}$$

4 ni olish uchun 20 ni 5 ga bo‘ling.

$$x^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2 x=-2$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$9x^{2}=4x^{2}+20$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$9x^{2}-4x^{2}=20$$

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

$$5x^{2}=20$$

Ikkala tarafdan 20 ni ayirish.

$$5x^{2}-20=0$$

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 -20 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni 5 marotabaga ko'paytirish.

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

-20 ni -20 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{400}}{2\times 5}$$

400 ning kvadrat ildizini chiqarish.

$$x=\frac{0±20}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±20}{10}$$

x=\frac{0±20}{10} tenglamasini yeching, bunda ± musbat. 20 ni 10 ga bo'lish.

$$x=2$$

x=\frac{0±20}{10} tenglamasini yeching, bunda ± manfiy. -20 ni 10 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

$$x=2 x=-2$$