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Identity (x-y)^2

if x-y=5 and ...

Question

if x-y=5 and xy=84,then find the value of x³ - y³

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Solution

Given :
x-y=5
xy=84
RTP :
By using the formula :
(x-y)³=x³-y³-3x²y+3xy²
x³-y³=(x-y)³+3x²y-3xy²
=(x-y)³+3xy[x-y]
by substituting the values, we get :
=[5]³+3x84[5]
=125 +1260
=1385
∴ x³-y³=1385

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