Question

If x-y=1 and x3-y3=61, then find the value of xy.

Answer 1

ANSWER

Given the equation

x+y=5 and xy=6

Find out the value of (x³-y³) is

To proof

As given the equation

put this in the x+y=5  equation

we get

thus

(x -2) (x -3) =0

x=2,x=3

When x=2

put in  x+y=5

y = 3

(x³-y³) = 8 - 2

      = -19

when

x=3

put in  x+y=5

(x³ -y³) = 27-8

        = 19

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Answer 2

Step-by-step explanation:

x - y = 1

x² + y² - 2xy = 1

x² + y² = 2xy + 1 -----(1)

x³ - y³ = 61

(x - y) (x² + xy + y²) = 61

1 ( x² + y² + xy ) = 61

from equation (1)

2xy + 1 + xy = 61

3xy = 60

xy = 20