SOLUTION: The sum of a number and 21 times it's reciprocal is -10. Find the number?
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Question 517039: The sum of a number and 21 times it's reciprocal is -10. Find the number?
Found 3 solutions by mananth, josmiceli, richwmiller:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let x be the number
x+21/x = -21
LCD = x
multiply by LCD
x^2+21=-21x
x^2+21x+21=0
Find the roots of the equation by quadratic formula
a= 1 ,b= 21 c 21
b^2-4ac= 441 - -84
b^2-4ac= 357
= 18.89
x1=( -21 + 18.89 )/ 2
x1= -1.05
x2=( -21 -18.89 ) / 2
x2= -19.947
m.ananth@hotmail.ca
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Multiply both sides by
Complete the square
Take the square root of both sides
and also
check answers:
OK
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x+21/x=-10
x^2+21+10x=0
x^2+10x+21=0
(x+7)*(x+3)=0
x=-7
x=-3
check -3
-3+21/-3=-10
-3-7=-10
-10=-10
ok
check -7
-7+21/-7=-10
-7-3=-10
-10=-10
ok
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