Допоможіть хоча б з якимось з них...
1) [tex] \left \{ {{ x^{2}+y^{2}=34}\atop{xy=15}} \right. [/tex]
2)[tex] \left \{ {{ x^{2}-2xy+y ^{2} =4} \atop { x^{2}+xy =4}} \right. [/tex]
3)[tex] \left \{ {{ x^{2}-3x+4 =y} \atop { y^{2}-3y+4 =x}} \right. [/tex]
1) [tex] \left \{ {{ x^{2}+y^{2}=34}\atop{xy=15}} \right. [/tex]
2)[tex] \left \{ {{ x^{2}-2xy+y ^{2} =4} \atop { x^{2}+xy =4}} \right. [/tex]
3)[tex] \left \{ {{ x^{2}-3x+4 =y} \atop { y^{2}-3y+4 =x}} \right. [/tex]
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1) х = 15/у(15/у)² + у² = 34 --- замена у² = а
225/а + а = 34
225 + а² - 34а = 0
по т.Виета корни 9 и 25
у² = 9 ⇒ у = +- 3 и тогда х = +-5
у² = 25 ⇒ у = +-5 и тогда х = +-3
Ответ: (5; 3), (-5; -3), (3; 5), (-3; -5)