x^2 +y^2 =13 x^2 −3xy+y^2 =35 find the value of x and y


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 30405 by scientist last updated on 22/Feb/18

$x^{2} + y^{2} = 13$ $x^{2} - 3 x y + y^{2} = 35$ $f i n d t h e v a l u e o f x a n d y$
	Answered by mrW2 last updated on 22/Feb/18
	$13−3xy=35 ⇒xy=((13−35)/3)=−((22)/3) (x+y)^2 =x^2 +y^2 +2xy=13−((44)/3)=−(5/3) ⇒x+y=±i(√(5/3)) (x−y)^2 =x^2 +y^2 −2xy=13+((44)/3)=((83)/3) ⇒x−y=±(√((83)/3)) ⇒x=(1/2)(±(√((83)/3))±i(√(5/3))) ⇒y=(1/2)(∓(√((83)/3))±i(√(5/3))) solution 1 { ((x=(1/2)((√((83)/3))+i(√(5/3))))),((y=(1/2)(−(√((83)/3))+i(√(5/3))))) :} solution 2 { ((x=(1/2)((√((83)/3))−i(√(5/3))))),((y=(1/2)(−(√((83)/3))−i(√(5/3))))) :} solution 3 { ((x=(1/2)(−(√((83)/3))+i(√(5/3))))),((y=(1/2)((√((83)/3))+i(√(5/3))))) :} solution 4 { ((x=(1/2)(−(√((83)/3))−i(√(5/3))))),((y=(1/2)((√((83)/3))−i(√(5/3))))) :}$
	$13 - 3 x y = 35$ $\Rightarrow x y = \frac{13 - 35}{3} = - \frac{22}{3}$ ${(x + y)}^{2} = x^{2} + y^{2} + 2 x y = 13 - \frac{44}{3} = - \frac{5}{3}$ $\Rightarrow x + y = \pm i \sqrt{\frac{5}{3}}$ ${(x - y)}^{2} = x^{2} + y^{2} - 2 x y = 13 + \frac{44}{3} = \frac{83}{3}$ $\Rightarrow x - y = \pm \sqrt{\frac{83}{3}}$ $\Rightarrow x = \frac{1}{2} (\pm \sqrt{\frac{83}{3}} \pm i \sqrt{\frac{5}{3}})$ $\Rightarrow y = \frac{1}{2} (\mp \sqrt{\frac{83}{3}} \pm i \sqrt{\frac{5}{3}})$ $s o l u t i o n 1 {\begin{cases} x = \frac{1}{2} (\sqrt{\frac{83}{3}} + i \sqrt{\frac{5}{3}}) \\ y = \frac{1}{2} (- \sqrt{\frac{83}{3}} + i \sqrt{\frac{5}{3}}) \end{cases}$ $s o l u t i o n 2 {\begin{cases} x = \frac{1}{2} (\sqrt{\frac{83}{3}} - i \sqrt{\frac{5}{3}}) \\ y = \frac{1}{2} (- \sqrt{\frac{83}{3}} - i \sqrt{\frac{5}{3}}) \end{cases}$ $s o l u t i o n 3 {\begin{cases} x = \frac{1}{2} (- \sqrt{\frac{83}{3}} + i \sqrt{\frac{5}{3}}) \\ y = \frac{1}{2} (\sqrt{\frac{83}{3}} + i \sqrt{\frac{5}{3}}) \end{cases}$ $s o l u t i o n 4 {\begin{cases} x = \frac{1}{2} (- \sqrt{\frac{83}{3}} - i \sqrt{\frac{5}{3}}) \\ y = \frac{1}{2} (\sqrt{\frac{83}{3}} - i \sqrt{\frac{5}{3}}) \end{cases}$
	Commented by Rasheed.Sindhi last updated on 22/Feb/18
	√3Я¥ ₪î¢3 §îЯ!
	Commented by mrW2 last updated on 22/Feb/18
	Thanks Sir!
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum