64-x^2=x^2 eching

$$64- { x }^{ 2 } = { x }^{ 2 }$$

x uchun yechish

$$x=4\sqrt{2}\approx 5,656854249$$

$$x=-4\sqrt{2}\approx -5,656854249$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish.

$$64-x^{2}-x^{2}=0$$

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

$$64-2x^{2}=0$$

Ikkala tarafdan 64 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-2x^{2}=-64$$

Ikki tarafini -2 ga bo‘ling.

$$x^{2}=\frac{-64}{-2}$$

32 ni olish uchun -64 ni -2 ga bo‘ling.

$$x^{2}=32$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=4\sqrt{2} x=-4\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x^{2} ni ayirish.

$$64-x^{2}-x^{2}=0$$

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

$$64-2x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-2x^{2}+64=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 0 ni b va 64 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 64}}{2\left(-2\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-2\right)\times 64}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{8\times 64}}{2\left(-2\right)}$$

8 ni 64 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{512}}{2\left(-2\right)}$$

512 ning kvadrat ildizini chiqarish.

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

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{0±16\sqrt{2}}{-4}$$

x=\frac{0±16\sqrt{2}}{-4} tenglamasini yeching, bunda ± musbat.

$$x=-4\sqrt{2}$$

x=\frac{0±16\sqrt{2}}{-4} tenglamasini yeching, bunda ± manfiy.

$$x=4\sqrt{2}$$

Tenglama yechildi.

$$x=-4\sqrt{2} x=4\sqrt{2}$$