9x^2-25=0 eching

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

x uchun yechish

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1,666666667$$

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1,666666667$$

Kvadratlar farqidan foydalangan qadamlar

Hisoblang: 9x^{2}-25. 9x^{2}-25 ni \left(3x\right)^{2}-5^{2} sifatida qaytadan yozish. Kvadratlarning farqini ushbu formula bilan hisoblash mumkin: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-5\right)\left(3x+5\right)=0$$

Tenglamani yechish uchun 3x-5=0 va 3x+5=0 ni yeching.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Kvadrat ildizini topish bo'yicha qadamlar

25 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

Ikki tarafini 9 ga bo‘ling.

$$x^{2}=\frac{25}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, 0 ni b va -25 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-25\right)}}{2\times 9}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 9\left(-25\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-36\left(-25\right)}}{2\times 9}$$

-36 ni -25 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{900}}{2\times 9}$$

900 ning kvadrat ildizini chiqarish.

$$x=\frac{0±30}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{0±30}{18}$$

x=\frac{0±30}{18} tenglamasini yeching, bunda ± musbat. \frac{30}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{3}$$

x=\frac{0±30}{18} tenglamasini yeching, bunda ± manfiy. \frac{-30}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{5}{3}$$

Tenglama yechildi.

$$x=\frac{5}{3} x=-\frac{5}{3}$$