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### 3 Answers

- KevinMLv 71 decade agoFavorite Answer
Multiply by r:

1 - 1/2 r^2 = 3/5 r

1/2 r^2 + 3/5 r - 1 = 0

5 r^2 + 6r - 10 = 0

And solve using the quadratic equation.

- 1 decade ago
First, get the left side into one fraction...that means getting a common denominator.

Because the denominators are r and 2, the common denominator is 2r.

Then, rewrite the fractions on the left with the new denominator:

(1/r)*(2/2) - (r/2)*(r/r) = 3/5

--> (2/2r) - (r^2/2r) = 3/5

--> (2 - r^2)/2r = 3/5

Cross multiply...

--> 5(2 - r^2) = 3*2r

--> 10 - 5r^2 = 6r

--> 5r^2 + 6r - 10 = 0

Use the quadratic formula to solve for r:

r = (-6 +- sqrt(36 +4*5*10)) / (2*5)

r = (-6 +- sqrt(236)) / 10

Simplifying, you get the set of two solutions....

r = { (-3 - sqrt(59)) / 5, (-3 + sqrt(59)) / 5 }

- 1 decade ago
1/r - r/2 = 3/5

*(10R) then

10 - 5r^2 = 6r

0= 5r^2 + 6r -10

here we have to use normal eq ax^2 + bx + c = 0

then you can get the answer.

here a= 5 ; b=6 ; c=-10