Created: 3 months ago |
Updated: 2 months ago
best des
Given yx+xy=6, let's find a common denominator to simplify:
xyx2+y2=6
Multiplying both sides by xy:
x2+y2=6xy
Now, we are asked to find y3x3+x3y3. We can use the identity (a+b)3=a3+b3+3ab(a+b) to expand:
(yx+xy)3=(y3x3+x3y3)+3(yx+xy)
Given yx+xy=6, we can substitute:
63=(y3x3+x3y3)+3×6
216=y3x3+x3y3+18
y3x3+x3y3=216−18
y3x3+x3y3=198
So, the value of y3x3+x3y3 is 198.
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