x+y=3
x²+y²=6
find : x³+y³
7.5
9
13.5
To solve for x³+y³, we can use the following formula:
x³+y³ = (x+y)(x²-xy+y²)
We already know that
x+y=3
and
x²+y²=6.
So, we can plug these values into the formula to get:
x³+y³ = (3)(6-xy)
We don't know the value of xy, but we can use the following equation to solve for it:
(x+y)² = x²+y²+2xy
We already know that
x+y=3
and
x²+y²=6.
So, we can plug these values into the equation to get:
(3)² = 6+2xy
Solving for xy, we get:
xy = 3/2
Now, we can plug this value into the formula for
x³+y³ to get:
x³+y³ = (3)(6-3/2)=3*4.5=13.5
Therefore, x³+y³ = 13.5
So, the answer on the image is correct.
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حل اخر
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x+y=3
x²+y²=6
x²+y²+2xy-2xy=6
(x²+2xy+y²)-2xy=6
(x+y)²-2xy=6
3²-2xy=6
9-2xy=6
2xy=9-6
2xy=3
xy=3/2=1,5
x³+y³=(x+y)(x²-xy+y²)=
3×(6-1,5)=3×4,5=13,5
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