1/2x+x=51/x eching

$$\frac{ 1 }{ 2 } x+x = \frac{ 51 }{ x }$$

x uchun yechish

$$x=\sqrt{34}\approx 5,830951895$$

$$x=-\sqrt{34}\approx -5,830951895$$

Kvadrat ildizini topish bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x ga, 2,x ning eng kichik karralisiga ko‘paytiring.

$$\frac{1}{2}x\times 2x+2xx=2\times 51$$

2 va 2 ni qisqartiring.

$$xx+2xx=2\times 51$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2xx=2\times 51$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2x^{2}=2\times 51$$

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

$$3x^{2}=2\times 51$$

102 hosil qilish uchun 2 va 51 ni ko'paytirish.

$$3x^{2}=102$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{102}{3}$$

34 ni olish uchun 102 ni 3 ga bo‘ling.

$$x^{2}=34$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{34} x=-\sqrt{34}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 2x ga, 2,x ning eng kichik karralisiga ko‘paytiring.

$$\frac{1}{2}x\times 2x+2xx=2\times 51$$

2 va 2 ni qisqartiring.

$$xx+2xx=2\times 51$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2xx=2\times 51$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x^{2}+2x^{2}=2\times 51$$

3x^{2} ni olish uchun x^{2} va 2x^{2} ni birlashtirish.

$$3x^{2}=2\times 51$$

102 hosil qilish uchun 2 va 51 ni ko'paytirish.

$$3x^{2}=102$$

Ikkala tarafdan 102 ni ayirish.

$$3x^{2}-102=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -102 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-102\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-102\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-102\right)}}{2\times 3}$$

-12 ni -102 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1224}}{2\times 3}$$

1224 ning kvadrat ildizini chiqarish.

$$x=\frac{0±6\sqrt{34}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±6\sqrt{34}}{6}$$

x=\frac{0±6\sqrt{34}}{6} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{34}$$

x=\frac{0±6\sqrt{34}}{6} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{34}$$

Tenglama yechildi.

$$x=\sqrt{34} x=-\sqrt{34}$$