radical time... :D
Algebra
Level
3
Find the real value(integral) of this expression.
The answer is 2.
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1 solution
let x be that expression:
y = ∛(√108 + 10)
y-20 = ∛(√108 - 10)
x^3 = y - 3(y^2)(y-20) + 3(y)(y-20) - (y-20)
x^3 = -3(y)(y-20)[y - (y-20)] + 20
x^3 = -3y(y-20)[x] + 20
x^3 = -3(∛(√108 + 10))( ∛(√108 - 10))[x] + 20
x^3 = -3( ∛8)[x] + 20
x^3 = -6x+20
x^3 + 6x - 20 = 0
x^3 - 2x^2 + 2x^2 + 6x - 20 = 0
(x-2)(x^2 + 2x + 10) = 0
x = {2}
So...
The Answer is 2: