6^2+(2*5+x)^2=4^2-(2*5-x)^2 eching

$$6 ^ { 2 } + ( 2 \cdot 5 + x ) ^ { 2 } = 4 ^ { 2 } - ( 2 \cdot 5 - x ) ^ { 2 }$$

x uchun yechish (complex solution)

$$x=-\sqrt{110}i\approx -0-10,488088482i$$

$$x=\sqrt{110}i\approx 10,488088482i$$

Kvadrat ildizini topish bo'yicha qadamlar

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$36+\left(2\times 5+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$36+\left(10+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(10+x\right)^{2} kengaytirilishi uchun ishlating.

$$36+100+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

136 olish uchun 36 va 100'ni qo'shing.

$$136+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

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

$$136+20x+x^{2}=16-\left(2\times 5-x\right)^{2}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$136+20x+x^{2}=16-\left(10-x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(10-x\right)^{2} kengaytirilishi uchun ishlating.

$$136+20x+x^{2}=16-\left(100-20x+x^{2}\right)$$

100-20x+x^{2} teskarisini topish uchun har birining teskarisini toping.

$$136+20x+x^{2}=16-100+20x-x^{2}$$

-84 olish uchun 16 dan 100 ni ayirish.

$$136+20x+x^{2}=-84+20x-x^{2}$$

Ikkala tarafdan 20x ni ayirish.

$$136+20x+x^{2}-20x=-84-x^{2}$$

0 ni olish uchun 20x va -20x ni birlashtirish.

$$136+x^{2}=-84-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$136+x^{2}+x^{2}=-84$$

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

$$136+2x^{2}=-84$$

Ikkala tarafdan 136 ni ayirish.

$$2x^{2}=-84-136$$

-220 olish uchun -84 dan 136 ni ayirish.

$$2x^{2}=-220$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{-220}{2}$$

-110 ni olish uchun -220 ni 2 ga bo‘ling.

$$x^{2}=-110$$

Tenglama yechildi.

$$x=\sqrt{110}i x=-\sqrt{110}i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 6 ga hisoblang va 36 ni qiymatni oling.

$$36+\left(2\times 5+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$36+\left(10+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(10+x\right)^{2} kengaytirilishi uchun ishlating.

$$36+100+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

136 olish uchun 36 va 100'ni qo'shing.

$$136+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

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

$$136+20x+x^{2}=16-\left(2\times 5-x\right)^{2}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$136+20x+x^{2}=16-\left(10-x\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(10-x\right)^{2} kengaytirilishi uchun ishlating.

$$136+20x+x^{2}=16-\left(100-20x+x^{2}\right)$$

100-20x+x^{2} teskarisini topish uchun har birining teskarisini toping.

$$136+20x+x^{2}=16-100+20x-x^{2}$$

-84 olish uchun 16 dan 100 ni ayirish.

$$136+20x+x^{2}=-84+20x-x^{2}$$

Ikkala tarafdan -84 ni ayirish.

$$136+20x+x^{2}-\left(-84\right)=20x-x^{2}$$

-84 ning teskarisi 84 ga teng.

$$136+20x+x^{2}+84=20x-x^{2}$$

Ikkala tarafdan 20x ni ayirish.

$$136+20x+x^{2}+84-20x=-x^{2}$$

220 olish uchun 136 va 84'ni qo'shing.

$$220+20x+x^{2}-20x=-x^{2}$$

0 ni olish uchun 20x va -20x ni birlashtirish.

$$220+x^{2}=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$220+x^{2}+x^{2}=0$$

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

$$220+2x^{2}=0$$

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.

$$2x^{2}+220=0$$

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 220 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 220}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\times 220}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\times 220}}{2\times 2}$$

-8 ni 220 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-1760}}{2\times 2}$$

-1760 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{110}i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{110}i}{4}$$

x=\frac{0±4\sqrt{110}i}{4} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{110}i$$

x=\frac{0±4\sqrt{110}i}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{110}i$$

Tenglama yechildi.

$$x=\sqrt{110}i x=-\sqrt{110}i$$