Question

If x+y=5 and xy=6 the value of (x3-y3) is

Answer 1

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Answer 2

ANSWER

Given the equation

x+y=5 and xy=6

Find out the value of (x³-y³) is

To proof

As given the equation

$y =\frac{6}{x}$

put this in the x+y=5  equation

we get

$x + \frac{6}{x} =5\\ x^{2} -5x +6 =0\\ x^{2} - 2x-3x+6 =0\\x(x-2)-3(x-2)=0$

thus

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

x=2,x=3

When x=2

put in  x+y=5

y = 3

(x³-y³) = 8 - 27

      = -19

when

x=3

put in  x+y=5

(x³ -y³) = 27-8

        = 19

Hence proved