Question

If x^2+y^2=13 and x*y= 6, find x^3+y^3
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Answer 1

Step-by-step explanation:

x2 +y2 = 13

x2 +y2 = (x+y)2-2xy

13 =( x+ y )2 - 2×6

13 = (x+y )2 -12

25 = (x+y )2

5 = x + y

now

x3 +y3 =( x+y )3 -3xy (x+ y )

= ( 5)3 - 3×6 × 5

= 125 - 90

= 35.

hence

x3 + y3 = 35