(sqrt{a}+sqrt{b})(sqrt{a}-sqrt{b})=a-b eching

$$( \sqrt { a } + \sqrt { b } ) ( \sqrt { a } - \sqrt { b } ) = a - b$$

a uchun yechish (complex solution)

$$a\in \mathrm{C}$$

Yechim qadamlari

Hisoblang: \left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{a}\right)^{2}-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-b=a-b$$

Ikkala tarafdan a ni ayirish.

$$a-b-a=-b$$

0 ni olish uchun a va -a ni birlashtirish.

$$-b=-b$$

-1ni ikki tarafidan bekor qilish.

$$b=b$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday a uchun to‘g‘ri.

$$a\in \mathrm{C}$$

b uchun yechish (complex solution)

$$b\in \mathrm{C}$$

Yechim qadamlari

Hisoblang: \left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{a}\right)^{2}-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-b=a-b$$

b ni ikki tarafga qo’shing.

$$a-b+b=a$$

0 ni olish uchun -b va b ni birlashtirish.

$$a=a$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday b uchun to‘g‘ri.

$$b\in \mathrm{C}$$

a uchun yechish

$$a\geq 0$$

$$b\geq 0$$

Yechim qadamlari

Hisoblang: \left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{a}\right)^{2}-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-b=a-b$$

Ikkala tarafdan a ni ayirish.

$$a-b-a=-b$$

0 ni olish uchun a va -a ni birlashtirish.

$$-b=-b$$

-1ni ikki tarafidan bekor qilish.

$$b=b$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday a uchun to‘g‘ri.

$$a\in \mathrm{R}$$

b uchun yechish

$$b\geq 0$$

$$a\geq 0$$

Yechim qadamlari

Hisoblang: \left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{a}\right)^{2}-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-\left(\sqrt{b}\right)^{2}=a-b$$

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

$$a-b=a-b$$

b ni ikki tarafga qo’shing.

$$a-b+b=a$$

0 ni olish uchun -b va b ni birlashtirish.

$$a=a$$

Shartlarni qayta saralash.

$$\text{true}$$

Bu har qanday b uchun to‘g‘ri.

$$b\in \mathrm{R}$$