4000(1+x)(1-x)=3940 eching

$$4000 ( 1 + x ) ( 1 - x ) = 3940$$

x uchun yechish

$$x=\frac{\sqrt{6}}{20}\approx 0,122474487$$

$$x=-\frac{\sqrt{6}}{20}\approx -0,122474487$$

Kvadrat ildizini topish bo'yicha qadamlar

4000 ga 1+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(4000+4000x\right)\left(1-x\right)=3940$$

4000+4000x ga 1-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4000-4000x^{2}=3940$$

Ikkala tarafdan 4000 ni ayirish.

$$-4000x^{2}=3940-4000$$

-60 olish uchun 3940 dan 4000 ni ayirish.

$$-4000x^{2}=-60$$

Ikki tarafini -4000 ga bo‘ling.

$$x^{2}=\frac{-60}{-4000}$$

\frac{-60}{-4000} ulushini -20 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}=\frac{3}{200}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{\sqrt{6}}{20} x=-\frac{\sqrt{6}}{20}$$

Kvadrat tenglamalaridan foydalanish qoidalari

4000 ga 1+x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(4000+4000x\right)\left(1-x\right)=3940$$

4000+4000x ga 1-x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4000-4000x^{2}=3940$$

Ikkala tarafdan 3940 ni ayirish.

$$4000-4000x^{2}-3940=0$$

60 olish uchun 4000 dan 3940 ni ayirish.

$$60-4000x^{2}=0$$

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.

$$-4000x^{2}+60=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -4000 ni a, 0 ni b va 60 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-4000\right)\times 60}}{2\left(-4000\right)}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-4000\right)\times 60}}{2\left(-4000\right)}$$

-4 ni -4000 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{16000\times 60}}{2\left(-4000\right)}$$

16000 ni 60 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{960000}}{2\left(-4000\right)}$$

960000 ning kvadrat ildizini chiqarish.

$$x=\frac{0±400\sqrt{6}}{2\left(-4000\right)}$$

2 ni -4000 marotabaga ko'paytirish.

$$x=\frac{0±400\sqrt{6}}{-8000}$$

x=\frac{0±400\sqrt{6}}{-8000} tenglamasini yeching, bunda ± musbat.

$$x=-\frac{\sqrt{6}}{20}$$

x=\frac{0±400\sqrt{6}}{-8000} tenglamasini yeching, bunda ± manfiy.

$$x=\frac{\sqrt{6}}{20}$$

Tenglama yechildi.

$$x=-\frac{\sqrt{6}}{20} x=\frac{\sqrt{6}}{20}$$