1=5-16t^2 eching

$$1 = 5 - 16 t ^ { 2 }$$

t uchun yechish

$$t=\frac{1}{2}=0,5$$

$$t=-\frac{1}{2}=-0,5$$

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$5-16t^{2}=1$$

Ikkala tarafdan 5 ni ayirish.

$$-16t^{2}=1-5$$

-4 olish uchun 1 dan 5 ni ayirish.

$$-16t^{2}=-4$$

Ikki tarafini -16 ga bo‘ling.

$$t^{2}=\frac{-4}{-16}$$

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

$$t^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$t=\frac{1}{2} t=-\frac{1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$5-16t^{2}=1$$

Ikkala tarafdan 1 ni ayirish.

$$5-16t^{2}-1=0$$

4 olish uchun 5 dan 1 ni ayirish.

$$4-16t^{2}=0$$

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.

$$-16t^{2}+4=0$$

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 4 ni c bilan almashtiring.

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

0 kvadratini chiqarish.

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

-4 ni -16 marotabaga ko'paytirish.

$$t=\frac{0±\sqrt{64\times 4}}{2\left(-16\right)}$$

64 ni 4 marotabaga ko'paytirish.

$$t=\frac{0±\sqrt{256}}{2\left(-16\right)}$$

256 ning kvadrat ildizini chiqarish.

$$t=\frac{0±16}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$t=\frac{0±16}{-32}$$

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

$$t=-\frac{1}{2}$$

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

$$t=\frac{1}{2}$$

Tenglama yechildi.

$$t=-\frac{1}{2} t=\frac{1}{2}$$