The roots of q quadratic $x^2-sqrt(20x)+2=0$ are c and d. Without using calculator show that $1/c+1/d=sqrt(5)$ ?

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$1/c+1/d=sqrt(5)$

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Answer 1 · 2018-01-22T09:43:08

See the proof below

If the roots of a quadratic equation $ax^2+bx+c=0$ are

$alpha$ and $beta$ then,

$alpha+beta=-b/a$

and

$alpha beta=c/a$

Here the quadratic equation is $x^2-sqrt20 x+2=0$

and the roots are $c$ and $d$

Therefore,

$c+d=sqrt20$

$cd=2$

so,

$1/c+1/d=(d+c)/(cd)$

$=(sqrt20)/2$

$=(2sqrt5)/2$

$=sqrt5$

$QED$