16k^4=40k^2-9 eching

$$16 k ^ { 4 } = 40 k ^ { 2 } - 9$$

k uchun yechish

$$k = -\frac{3}{2} = -1\frac{1}{2} = -1,5$$

$$k = \frac{3}{2} = 1\frac{1}{2} = 1,5$$

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

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 40k^{2} ni ayirish.

$$16k^{4}-40k^{2}=-9$$

9 ni ikki tarafga qo’shing.

$$16k^{4}-40k^{2}+9=0$$

k^{2} uchun t ni almashtiring.

$$16t^{2}-40t+9=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 16 ni, b uchun -40 ni va c uchun 9 ni ayiring.

$$t=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 16\times 9}}{2\times 16}$$

Hisoblarni amalga oshiring.

$$t=\frac{40±32}{32}$$

t=\frac{40±32}{32} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

$$t=\frac{9}{4} t=\frac{1}{4}$$

k=t^{2} boʻlganda, yechimlar har bir t uchun k=±\sqrt{t} hisoblanishi orqali olinadi.

$$k=\frac{3}{2} k=-\frac{3}{2} k=\frac{1}{2} k=-\frac{1}{2}$$