25x=sqrt{49x^2+48^2} eching

$$25x= \sqrt{ 49 { x }^{ 2 } + { 48 }^{ 2 } }$$

x uchun yechish

$$x=2$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(25x\right)^{2}=\left(\sqrt{49x^{2}+48^{2}}\right)^{2}$$

\left(25x\right)^{2} ni kengaytirish.

$$25^{2}x^{2}=\left(\sqrt{49x^{2}+48^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini 25 ga hisoblang va 625 ni qiymatni oling.

$$625x^{2}=\left(\sqrt{49x^{2}+48^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini 48 ga hisoblang va 2304 ni qiymatni oling.

$$625x^{2}=\left(\sqrt{49x^{2}+2304}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{49x^{2}+2304} ga hisoblang va 49x^{2}+2304 ni qiymatni oling.

$$625x^{2}=49x^{2}+2304$$

Ikkala tarafdan 49x^{2} ni ayirish.

$$625x^{2}-49x^{2}=2304$$

576x^{2} ni olish uchun 625x^{2} va -49x^{2} ni birlashtirish.

$$576x^{2}=2304$$

Ikkala tarafdan 2304 ni ayirish.

$$576x^{2}-2304=0$$

Ikki tarafini 576 ga bo‘ling.

$$x^{2}-4=0$$

Hisoblang: x^{2}-4. x^{2}-4 ni x^{2}-2^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

Tenglamani yechish uchun x-2=0 va x+2=0 ni yeching.

$$x=2 x=-2$$

25x=\sqrt{49x^{2}+48^{2}} tenglamasida x uchun 2 ni almashtiring.

$$25\times 2=\sqrt{49\times 2^{2}+48^{2}}$$

Qisqartirish. x=2 tenglamani qoniqtiradi.

$$50=50$$

25x=\sqrt{49x^{2}+48^{2}} tenglamasida x uchun -2 ni almashtiring.

$$25\left(-2\right)=\sqrt{49\left(-2\right)^{2}+48^{2}}$$

Qisqartirish. x=-2 qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$-50=50$$

25x=\sqrt{49x^{2}+2304} tenglamasi noyob yechimga ega.

$$x=2$$