What is the value of a^2 +b^2 if ax+by=3 bx−ay = 4 and x^2 +y^2 = 4


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Question Number 136607 by EDWIN88 last updated on 23/Mar/21

$What is the value of a^{2} + b^{2} if ax + by = 3$ $bx - ay = 4 and x^{2} + y^{2} = 4$
	Answered by MJS_new last updated on 24/Mar/21
	${ ((ax+by=3)),((bx−ay=4)) :} ⇔ { ((a=((3x−4y)/(x^2 +y^2 )))),((b=((4x+3y)/(x^2 +y^2 )))) :} ⇒ a^2 +b^2 =((25)/(x^2 +y^2 ))=((25)/4)$
	${\begin{cases} a x + b y = 3 \\ b x - a y = 4 \end{cases} \Leftrightarrow {\begin{cases} a = \frac{3 x - 4 y}{x^{2} + y^{2}} \\ b = \frac{4 x + 3 y}{x^{2} + y^{2}} \end{cases} \Rightarrow a^{2} + b^{2} = \frac{25}{x^{2} + y^{2}} = \frac{25}{4}$
	Answered by mindispower last updated on 24/Mar/21

	${(a x + b y)}^{2} + {(b x - a y)}^{2} = (a^{2} + b^{2}) (x^{2} + y^{2}) . . .$
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