Question

If x=
√m +1 + √m-1
√m+1 - √m-1
prove that x - 3mx2 + 3x =m.​

Answer 1

x³ - 3mx² + 3x - m = 0 if x = (∛(m+1)  + ∛(m-1) ) /(∛(m + 1) - ∛(m-1)

Step-by-step explanation:

x = (∛(m+1)  + ∛(m-1) ) /(∛(m + 1) - ∛(m-1)

=> x/1 =  (∛(m+1)  + ∛(m-1) ) /(∛(m + 1) - ∛(m-1))

using componendo & dividendo

=> (x + 1) / (x - 1) = 2∛(m+1) / 2∛(m-1)

=> (x + 1) / (x - 1) = ∛(m+1) / ∛(m-1)

cubing both sides

=> (x + 1)³/(x - 1)³ = (m + 1)/(m -1)

=>  (m + 1)/(m -1) = (x³ + 3x²  + 3x + 1  )/(x³ - 3x² + 3x - 1)

using componendo & dividendo

=> 2m / 2 = 2(x³ + 3x)/2(3x² + 1)

=> m = (x³ + 3x)/(3x² + 1)

=> 3mx² + m = x³ + 3x

=> x³ - 3mx² + 3x - m = 0

Learn more:

√5x+√2x-6/√5x-√2x-6=4 find x using componendo and dividendo ...

If 4a+7b/4c+7d=4a-7b/4c-7d then prove that a:b::c:d

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