Question

Ravi sold his motor cycle to Kavi at a loss of 28%. Kavi spent 1680 on its repairs and sold the motor cycle to Pradeep for 35910, there by making a profit of 12.5%, find the cost price of the motor cycle for Ravi.
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Answer 1

Answer:

(x-1/x)³ = x³-1/x³ - 3×x×1/x(1–1/x)

or (x-1/x)³ = x³-1/x³ - 3(1–1/x)

or (x-1/x)³ = 14 - 3(1–1/x) . . . . [Given, x³-1/x³ = 14]

Let x-1/x = a

Therefore a³ = 14 - 3a

or a³+3a-14 =0

or a³-2a²+2a²-4a+7a-14 =0

or a²(a-2) +2a(a-2) +7(a-2) =0

or (a-2)(a²+2a+7) =0

or a-2 = 0/(a²+2a+7)

or a = 2

So x-1/x = 2