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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 by Rio Michael last updated on 06/Oct/19

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