p*q=sqrt{8040}(p+q) eching

$$p \cdot q = \sqrt { 8040 } ( p + q )$$

p uchun yechish

$$p=\frac{2\sqrt{2010}q}{q-2\sqrt{2010}}$$

$$q\neq 2\sqrt{2010}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Faktor: 8040=2^{2}\times 2010. \sqrt{2^{2}\times 2010} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2010} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$pq=2\sqrt{2010}\left(p+q\right)$$

2\sqrt{2010} ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$pq=2\sqrt{2010}p+2\sqrt{2010}q$$

Ikkala tarafdan 2\sqrt{2010}p ni ayirish.

$$pq-2\sqrt{2010}p=2\sqrt{2010}q$$

p'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(q-2\sqrt{2010}\right)p=2\sqrt{2010}q$$

Ikki tarafini q-2\sqrt{2010} ga bo‘ling.

$$\frac{\left(q-2\sqrt{2010}\right)p}{q-2\sqrt{2010}}=\frac{2\sqrt{2010}q}{q-2\sqrt{2010}}$$

q-2\sqrt{2010} ga bo'lish q-2\sqrt{2010} ga ko'paytirishni bekor qiladi.

$$p=\frac{2\sqrt{2010}q}{q-2\sqrt{2010}}$$

q uchun yechish

$$q=\frac{2\sqrt{2010}p}{p-2\sqrt{2010}}$$

$$p\neq 2\sqrt{2010}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Faktor: 8040=2^{2}\times 2010. \sqrt{2^{2}\times 2010} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2010} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$pq=2\sqrt{2010}\left(p+q\right)$$

2\sqrt{2010} ga p+q ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$pq=2\sqrt{2010}p+2\sqrt{2010}q$$

Ikkala tarafdan 2\sqrt{2010}q ni ayirish.

$$pq-2\sqrt{2010}q=2\sqrt{2010}p$$

q'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(p-2\sqrt{2010}\right)q=2\sqrt{2010}p$$

Ikki tarafini p-2\sqrt{2010} ga bo‘ling.

$$\frac{\left(p-2\sqrt{2010}\right)q}{p-2\sqrt{2010}}=\frac{2\sqrt{2010}p}{p-2\sqrt{2010}}$$

p-2\sqrt{2010} ga bo'lish p-2\sqrt{2010} ga ko'paytirishni bekor qiladi.

$$q=\frac{2\sqrt{2010}p}{p-2\sqrt{2010}}$$