left(3xright)^2+6^2=left(5xright)^2 eching

$${ \left(3x \right) }^{ 2 } + { 6 }^{ 2 } = { \left(5x \right) }^{ 2 }$$

x uchun yechish

$$x = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

Kvadrat ildizini topish bo'yicha qadamlar

\left(3x\right)^{2} ni kengaytirish.

$$3^{2}x^{2}+6^{2}=\left(5x\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9x^{2}+6^{2}=\left(5x\right)^{2}$$

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

$$9x^{2}+36=\left(5x\right)^{2}$$

\left(5x\right)^{2} ni kengaytirish.

$$9x^{2}+36=5^{2}x^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$9x^{2}+36=25x^{2}$$

Ikkala tarafdan 25x^{2} ni ayirish.

$$9x^{2}+36-25x^{2}=0$$

-16x^{2} ni olish uchun 9x^{2} va -25x^{2} ni birlashtirish.

$$-16x^{2}+36=0$$

Ikkala tarafdan 36 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-16x^{2}=-36$$

Ikki tarafini -16 ga bo‘ling.

$$x^{2}=\frac{-36}{-16}$$

\frac{-36}{-16} ulushini -4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{3}{2} x=-\frac{3}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(3x\right)^{2} ni kengaytirish.

$$3^{2}x^{2}+6^{2}=\left(5x\right)^{2}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$9x^{2}+6^{2}=\left(5x\right)^{2}$$

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

$$9x^{2}+36=\left(5x\right)^{2}$$

\left(5x\right)^{2} ni kengaytirish.

$$9x^{2}+36=5^{2}x^{2}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$9x^{2}+36=25x^{2}$$

Ikkala tarafdan 25x^{2} ni ayirish.

$$9x^{2}+36-25x^{2}=0$$

-16x^{2} ni olish uchun 9x^{2} va -25x^{2} ni birlashtirish.

$$-16x^{2}+36=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -16 ni a, 0 ni b va 36 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 36}}{2\left(-16\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-16\right)\times 36}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{64\times 36}}{2\left(-16\right)}$$

64 ni 36 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{2304}}{2\left(-16\right)}$$

2304 ning kvadrat ildizini chiqarish.

$$x=\frac{0±48}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$x=\frac{0±48}{-32}$$

x=\frac{0±48}{-32} tenglamasini yeching, bunda ± musbat. \frac{48}{-32} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{3}{2}$$

x=\frac{0±48}{-32} tenglamasini yeching, bunda ± manfiy. \frac{-48}{-32} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{2}$$

Tenglama yechildi.

$$x=-\frac{3}{2} x=\frac{3}{2}$$