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Question Number 214419 by 2universe456 last updated on 08/Dec/24

	Answered by golsendro last updated on 08/Dec/24
	${ ((x^2 +y^2 +2xy=25)),((x^2 +y^2 +47=10xy)) :}⇒2xy+47=10xy+25 8xy= 22⇒4xy=11 4x(5−x)=11 ⇒4x^2 −20x+11=0 x_1 =(1/2)(5+(√(14)) ) ; x_2 =(1/2)(5−(√(14)) ) y_1 =5−(5/2)−(1/2)(√(14)) =(1/2)(5−(√(14)) ) y_2 = (1/2)(5+(√(14)) ) T= xy= (1/4)(25−14)= ((11)/4) H= x+y = 5 V= 2 ⇒V+T+H = 7+((11)/4) = ((39)/4)$
	${\begin{cases} x^{2} + y^{2} + 2 xy = 25 \\ x^{2} + y^{2} + 47 = 10 xy \end{cases} \Rightarrow 2 xy + 47 = 10 xy + 25$ $8 xy = 22 \Rightarrow 4 xy = 11$ $4 x (5 - x) = 11 \Rightarrow {4 x}^{2} - 20 x + 11 = 0$ $x_{1} = \frac{1}{2} (5 + \sqrt{14}); x_{2} = \frac{1}{2} (5 - \sqrt{14})$ $y_{1} = 5 - \frac{5}{2} - \frac{1}{2} \sqrt{14} = \frac{1}{2} (5 - \sqrt{14})$ $y_{2} = \frac{1}{2} (5 + \sqrt{14})$ $T = xy = \frac{1}{4} (25 - 14) = \frac{11}{4}$ $H = x + y = 5$ $V = 2 \Rightarrow V + T + H = 7 + \frac{11}{4} = \frac{39}{4}$
	Commented by Abdullahrussell last updated on 09/Dec/24

	$x y = 6$
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