A sixth degree equation

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Question from Farzan, a teacher:

Dear friends
I need to solve this equation with an understandable method for high-school students :
(6.67*5.98*10^13/(R^2*2))^2 + 6.67*5.98*10^13/R = (7.27*10^-5*R)^2
please solve this problem if you have time.

Frazan,

Let a = 6.67*5.98*10¹³ and b = 7.27*10^-5 then the equation becomes

[a/(2R²)]² + a/R = (bR)²

a²/(4R⁴) + a/R = b²R²

Multiply both sides by 4R⁴ to get

a² + 4aR³ = 4b²R⁶

Now let x = R³ and the equation becomes

4b²x² - 4ax - a² = 0

Solve for x and then R is the cube root of x.

Harley

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