34-y=120/y eching

$$34 - y = \frac { 120 } { y }$$

y uchun yechish

$$y=4$$

$$y=30$$

Kvadrat tenglamalaridan foydalanish qoidalari

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$y\times 34-yy=120$$

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$y\times 34-y^{2}=120$$

Ikkala tarafdan 120 ni ayirish.

$$y\times 34-y^{2}-120=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-y^{2}+34y-120=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 34 ni b va -120 ni c bilan almashtiring.

$$y=\frac{-34±\sqrt{34^{2}-4\left(-1\right)\left(-120\right)}}{2\left(-1\right)}$$

34 kvadratini chiqarish.

$$y=\frac{-34±\sqrt{1156-4\left(-1\right)\left(-120\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$y=\frac{-34±\sqrt{1156+4\left(-120\right)}}{2\left(-1\right)}$$

4 ni -120 marotabaga ko'paytirish.

$$y=\frac{-34±\sqrt{1156-480}}{2\left(-1\right)}$$

1156 ni -480 ga qo'shish.

$$y=\frac{-34±\sqrt{676}}{2\left(-1\right)}$$

676 ning kvadrat ildizini chiqarish.

$$y=\frac{-34±26}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$y=\frac{-34±26}{-2}$$

y=\frac{-34±26}{-2} tenglamasini yeching, bunda ± musbat. -34 ni 26 ga qo'shish.

$$y=-\frac{8}{-2}$$

-8 ni -2 ga bo'lish.

$$y=4$$

y=\frac{-34±26}{-2} tenglamasini yeching, bunda ± manfiy. -34 dan 26 ni ayirish.

$$y=-\frac{60}{-2}$$

-60 ni -2 ga bo'lish.

$$y=30$$

Tenglama yechildi.

$$y=4 y=30$$

Kvadratni yakunlash bo'yicha qadamlar

y qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini y ga ko'paytirish.

$$y\times 34-yy=120$$

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$y\times 34-y^{2}=120$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-y^{2}+34y=120$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-y^{2}+34y}{-1}=\frac{120}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$y^{2}+\frac{34}{-1}y=\frac{120}{-1}$$

34 ni -1 ga bo'lish.

$$y^{2}-34y=\frac{120}{-1}$$

120 ni -1 ga bo'lish.

$$y^{2}-34y=-120$$

-34 ni bo‘lish, x shartining koeffitsienti, 2 ga -17 olish uchun. Keyin, -17 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$y^{2}-34y+\left(-17\right)^{2}=-120+\left(-17\right)^{2}$$

-17 kvadratini chiqarish.

$$y^{2}-34y+289=-120+289$$

-120 ni 289 ga qo'shish.

$$y^{2}-34y+289=169$$

y^{2}-34y+289 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(y-17\right)^{2}=169$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(y-17\right)^{2}}=\sqrt{169}$$

Qisqartirish.

$$y-17=13 y-17=-13$$

17 ni tenglamaning ikkala tarafiga qo'shish.

$$y=30 y=4$$