given that α and β are roots of the equation x^2 −5x + 4 =0 α>0 and β >0 find an equation whose roots are (√α) and (√β) how do i find (√(α )) + (√β)


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Question Number 70617 by Rio Michael last updated on 06/Oct/19

$g i v e n t h a t α a n d β a r e r o o t s o f t h e e q u a t i o n x^{2} - 5 x + 4 = 0$ $α > 0 a n d β > 0$ $f i n d a n e q u a t i o n w h o s e r o o t s a r e \sqrt{α} a n d \sqrt{β}$ $h o w d o i f i n d \sqrt{α} + \sqrt{β}$
	Answered by mr W last updated on 06/Oct/19

	$α β = 4 \Rightarrow \sqrt{α} \sqrt{β} = 2$ $α + β = 5$ $\Rightarrow {(\sqrt{α})}^{2} + {(\sqrt{β})}^{2} = 5$ $\Rightarrow {(\sqrt{α})}^{2} + {(\sqrt{β})}^{2} + 2 \sqrt{α} \sqrt{β} = 5 + 2 \sqrt{α} \sqrt{β}$ $\Rightarrow {(\sqrt{α} + \sqrt{β})}^{2} = 5 + 2 \times 2 = 9$ $\Rightarrow \sqrt{α} + \sqrt{β} = \sqrt{9} = 3$ $t h e e q n . w i t h r o o t s \sqrt{α} a n d \sqrt{β} i s$ $x^{2} - 3 x + 2 = 0$
	Commented byRio Michael last updated on 06/Oct/19

	$t h a n k y i u s o m u c h m r W$
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