25^2/75^2+x^2/45=1 eching

$$\frac{ { 25 }^{ 2 } }{ { 75 }^{ 2 } } + \frac{ { x }^{ 2 } }{ 45 } =1$$

x uchun yechish

$$x=2\sqrt{10}\approx 6,32455532$$

$$x=-2\sqrt{10}\approx -6,32455532$$

Kvadrat ildizini topish bo'yicha qadamlar

Tenglamaning ikkala tarafini 45 ga ko'paytirish.

$$\frac{1}{125}\times 25^{2}+x^{2}=45$$

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

$$\frac{1}{125}\times 625+x^{2}=45$$

5 hosil qilish uchun \frac{1}{125} va 625 ni ko'paytirish.

$$5+x^{2}=45$$

Ikkala tarafdan 5 ni ayirish.

$$x^{2}=45-5$$

40 olish uchun 45 dan 5 ni ayirish.

$$x^{2}=40$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=2\sqrt{10} x=-2\sqrt{10}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 45 ga ko'paytirish.

$$\frac{1}{125}\times 25^{2}+x^{2}=45$$

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

$$\frac{1}{125}\times 625+x^{2}=45$$

5 hosil qilish uchun \frac{1}{125} va 625 ni ko'paytirish.

$$5+x^{2}=45$$

Ikkala tarafdan 45 ni ayirish.

$$5+x^{2}-45=0$$

-40 olish uchun 5 dan 45 ni ayirish.

$$-40+x^{2}=0$$

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.

$$x^{2}-40=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -40 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-40\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-40\right)}}{2}$$

-4 ni -40 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{160}}{2}$$

160 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{10}}{2}$$

x=\frac{0±4\sqrt{10}}{2} tenglamasini yeching, bunda ± musbat.

$$x=2\sqrt{10}$$

x=\frac{0±4\sqrt{10}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-2\sqrt{10}$$

Tenglama yechildi.

$$x=2\sqrt{10} x=-2\sqrt{10}$$