Pretty easy
If x+y=7, and xy=8 what is the value of x^3+y^3=?
The answer is 175.
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2 solutions
- Simplifying the binomial theorem, we get:
( x + y ) 3 = x 3 + 3 x y ( x + y ) + y 3
- Substituting known values and rearranging, we get:
( 7 ) 3 ( 7 ) 3 − 3 ( 8 ) ( 7 ) 3 4 3 − 1 6 8 = x 3 + 3 ( 8 ) ( 7 ) + y 3 = x 3 + y 3 = x 3 + y 3
- After simplifying we get:
x 3 + y 3 = 1 7 5