1/2(4^2+(8-x)^2+(4+x)^2)=88 eching

$$\frac { 1 } { 2 } ( 4 ^ { 2 } + ( 8 - x ) ^ { 2 } + ( 4 + x ) ^ { 2 } ) = 88$$

x uchun yechish

$$x=2\sqrt{11}+2\approx 8,633249581$$

$$x=2-2\sqrt{11}\approx -4,633249581$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikki tarafini 2 va teskari kasri \frac{1}{2} ga ko‘paytiring.

$$4^{2}+\left(8-x\right)^{2}+\left(4+x\right)^{2}=88\times 2$$

176 hosil qilish uchun 88 va 2 ni ko'paytirish.

$$4^{2}+\left(8-x\right)^{2}+\left(4+x\right)^{2}=176$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16+\left(8-x\right)^{2}+\left(4+x\right)^{2}=176$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(8-x\right)^{2} kengaytirilishi uchun ishlating.

$$16+64-16x+x^{2}+\left(4+x\right)^{2}=176$$

80 olish uchun 16 va 64'ni qo'shing.

$$80-16x+x^{2}+\left(4+x\right)^{2}=176$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(4+x\right)^{2} kengaytirilishi uchun ishlating.

$$80-16x+x^{2}+16+8x+x^{2}=176$$

96 olish uchun 80 va 16'ni qo'shing.

$$96-16x+x^{2}+8x+x^{2}=176$$

-8x ni olish uchun -16x va 8x ni birlashtirish.

$$96-8x+x^{2}+x^{2}=176$$

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

$$96-8x+2x^{2}=176$$

Ikkala tarafdan 176 ni ayirish.

$$96-8x+2x^{2}-176=0$$

-80 olish uchun 96 dan 176 ni ayirish.

$$-80-8x+2x^{2}=0$$

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.

$$2x^{2}-8x-80=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -8 ni b va -80 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-80\right)}}{2\times 2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-80\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-80\right)}}{2\times 2}$$

-8 ni -80 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+640}}{2\times 2}$$

64 ni 640 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{704}}{2\times 2}$$

704 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±8\sqrt{11}}{2\times 2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±8\sqrt{11}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{8±8\sqrt{11}}{4}$$

x=\frac{8±8\sqrt{11}}{4} tenglamasini yeching, bunda ± musbat. 8 ni 8\sqrt{11} ga qo'shish.

$$x=\frac{8\sqrt{11}+8}{4}$$

8+8\sqrt{11} ni 4 ga bo'lish.

$$x=2\sqrt{11}+2$$

x=\frac{8±8\sqrt{11}}{4} tenglamasini yeching, bunda ± manfiy. 8 dan 8\sqrt{11} ni ayirish.

$$x=\frac{8-8\sqrt{11}}{4}$$

8-8\sqrt{11} ni 4 ga bo'lish.

$$x=2-2\sqrt{11}$$

Tenglama yechildi.

$$x=2\sqrt{11}+2 x=2-2\sqrt{11}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikki tarafini 2 va teskari kasri \frac{1}{2} ga ko‘paytiring.

$$4^{2}+\left(8-x\right)^{2}+\left(4+x\right)^{2}=88\times 2$$

176 hosil qilish uchun 88 va 2 ni ko'paytirish.

$$4^{2}+\left(8-x\right)^{2}+\left(4+x\right)^{2}=176$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$16+\left(8-x\right)^{2}+\left(4+x\right)^{2}=176$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(8-x\right)^{2} kengaytirilishi uchun ishlating.

$$16+64-16x+x^{2}+\left(4+x\right)^{2}=176$$

80 olish uchun 16 va 64'ni qo'shing.

$$80-16x+x^{2}+\left(4+x\right)^{2}=176$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(4+x\right)^{2} kengaytirilishi uchun ishlating.

$$80-16x+x^{2}+16+8x+x^{2}=176$$

96 olish uchun 80 va 16'ni qo'shing.

$$96-16x+x^{2}+8x+x^{2}=176$$

-8x ni olish uchun -16x va 8x ni birlashtirish.

$$96-8x+x^{2}+x^{2}=176$$

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

$$96-8x+2x^{2}=176$$

Ikkala tarafdan 96 ni ayirish.

$$-8x+2x^{2}=176-96$$

80 olish uchun 176 dan 96 ni ayirish.

$$-8x+2x^{2}=80$$

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

$$2x^{2}-8x=80$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}-8x}{2}=\frac{80}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{8}{2}\right)x=\frac{80}{2}$$

-8 ni 2 ga bo'lish.

$$x^{2}-4x=\frac{80}{2}$$

80 ni 2 ga bo'lish.

$$x^{2}-4x=40$$

-4 ni bo‘lish, x shartining koeffitsienti, 2 ga -2 olish uchun. Keyin, -2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-4x+\left(-2\right)^{2}=40+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=40+4$$

40 ni 4 ga qo'shish.

$$x^{2}-4x+4=44$$

x^{2}-4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-2\right)^{2}=44$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{44}$$

Qisqartirish.

$$x-2=2\sqrt{11} x-2=-2\sqrt{11}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{11}+2 x=2-2\sqrt{11}$$