5/w^2-32=6/w^2+56 eching

$$\frac { 5 } { w ^ { 2 } } - 32 = \frac { 6 } { w ^ { 2 } } + 56$$

w uchun yechish

$$w=-\frac{\sqrt{22}i}{44}\approx -0-0,106600358i$$

$$w=\frac{\sqrt{22}i}{44}\approx 0,106600358i$$

Kvadrat ildizini topish bo'yicha qadamlar

w qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini w^{2} ga ko'paytirish.

$$5+w^{2}\left(-32\right)=6+w^{2}\times 56$$

Ikkala tarafdan w^{2}\times 56 ni ayirish.

$$5+w^{2}\left(-32\right)-w^{2}\times 56=6$$

-88w^{2} ni olish uchun w^{2}\left(-32\right) va -w^{2}\times 56 ni birlashtirish.

$$5-88w^{2}=6$$

Ikkala tarafdan 5 ni ayirish.

$$-88w^{2}=6-5$$

1 olish uchun 6 dan 5 ni ayirish.

$$-88w^{2}=1$$

Ikki tarafini -88 ga bo‘ling.

$$w^{2}=-\frac{1}{88}$$

Tenglama yechildi.

$$w=\frac{\sqrt{22}i}{44} w=-\frac{\sqrt{22}i}{44}$$

Kvadrat tenglamalaridan foydalanish qoidalari

w qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini w^{2} ga ko'paytirish.

$$5+w^{2}\left(-32\right)=6+w^{2}\times 56$$

Ikkala tarafdan 6 ni ayirish.

$$5+w^{2}\left(-32\right)-6=w^{2}\times 56$$

-1 olish uchun 5 dan 6 ni ayirish.

$$-1+w^{2}\left(-32\right)=w^{2}\times 56$$

Ikkala tarafdan w^{2}\times 56 ni ayirish.

$$-1+w^{2}\left(-32\right)-w^{2}\times 56=0$$

-88w^{2} ni olish uchun w^{2}\left(-32\right) va -w^{2}\times 56 ni birlashtirish.

$$-1-88w^{2}=0$$

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.

$$-88w^{2}-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -88 ni a, 0 ni b va -1 ni c bilan almashtiring.

$$w=\frac{0±\sqrt{0^{2}-4\left(-88\right)\left(-1\right)}}{2\left(-88\right)}$$

0 kvadratini chiqarish.

$$w=\frac{0±\sqrt{-4\left(-88\right)\left(-1\right)}}{2\left(-88\right)}$$

-4 ni -88 marotabaga ko'paytirish.

$$w=\frac{0±\sqrt{352\left(-1\right)}}{2\left(-88\right)}$$

352 ni -1 marotabaga ko'paytirish.

$$w=\frac{0±\sqrt{-352}}{2\left(-88\right)}$$

-352 ning kvadrat ildizini chiqarish.

$$w=\frac{0±4\sqrt{22}i}{2\left(-88\right)}$$

2 ni -88 marotabaga ko'paytirish.

$$w=\frac{0±4\sqrt{22}i}{-176}$$

w=\frac{0±4\sqrt{22}i}{-176} tenglamasini yeching, bunda ± musbat.

$$w=-\frac{\sqrt{22}i}{44}$$

w=\frac{0±4\sqrt{22}i}{-176} tenglamasini yeching, bunda ± manfiy.

$$w=\frac{\sqrt{22}i}{44}$$

Tenglama yechildi.

$$w=-\frac{\sqrt{22}i}{44} w=\frac{\sqrt{22}i}{44}$$