sqrt{x+5}=x eching

$$\sqrt{ x+5 } =x$$

x uchun yechish

$$x = \frac{\sqrt{21} + 1}{2} \approx 2,791287847$$

Yechim qadamlari

Tenglamaning ikkala taraf kvadratini chiqarish.

$$\left(\sqrt{x+5}\right)^{2}=x^{2}$$

2 daraja ko‘rsatkichini \sqrt{x+5} ga hisoblang va x+5 ni qiymatni oling.

$$x+5=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$x+5-x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-x^{2}+x+5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 1 ni b va 5 ni c bilan almashtiring.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+4\times 5}}{2\left(-1\right)}$$

4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+20}}{2\left(-1\right)}$$

1 ni 20 ga qo'shish.

$$x=\frac{-1±\sqrt{21}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{21}}{-2}$$

x=\frac{-1±\sqrt{21}}{-2} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{21} ga qo'shish.

$$x=\frac{\sqrt{21}-1}{-2}$$

-1+\sqrt{21} ni -2 ga bo'lish.

$$x=\frac{1-\sqrt{21}}{2}$$

x=\frac{-1±\sqrt{21}}{-2} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{21} ni ayirish.

$$x=\frac{-\sqrt{21}-1}{-2}$$

-1-\sqrt{21} ni -2 ga bo'lish.

$$x=\frac{\sqrt{21}+1}{2}$$

Tenglama yechildi.

$$x=\frac{1-\sqrt{21}}{2} x=\frac{\sqrt{21}+1}{2}$$

\sqrt{x+5}=x tenglamasida x uchun \frac{1-\sqrt{21}}{2} ni almashtiring.

$$\sqrt{\frac{1-\sqrt{21}}{2}+5}=\frac{1-\sqrt{21}}{2}$$

Qisqartirish. x=\frac{1-\sqrt{21}}{2} qiymati bu tenglamani qoniqtirmaydi, chunki oʻng va chap tarafdagi belgilar bir-biriga qarama-qarshi.

$$-\left(\frac{1}{2}-\frac{1}{2}\times 21^{\frac{1}{2}}\right)=\frac{1}{2}-\frac{1}{2}\times 21^{\frac{1}{2}}$$

\sqrt{x+5}=x tenglamasida x uchun \frac{\sqrt{21}+1}{2} ni almashtiring.

$$\sqrt{\frac{\sqrt{21}+1}{2}+5}=\frac{\sqrt{21}+1}{2}$$

Qisqartirish. x=\frac{\sqrt{21}+1}{2} tenglamani qoniqtiradi.

$$\frac{1}{2}+\frac{1}{2}\times 21^{\frac{1}{2}}=\frac{1}{2}\times 21^{\frac{1}{2}}+\frac{1}{2}$$

\sqrt{x+5}=x tenglamasi noyob yechimga ega.

$$x=\frac{\sqrt{21}+1}{2}$$