Q4
If 2x + 3y = 5 and xy = 2, then find the value of 8x3+27y3
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Answer:
=8x³+27y³
=(2x)³+(3y)³
=a³+b³=(a+b) (a²-ab+b²)
=(2x+3y)[(2x²)-2x*3y+(3y)²]
[2x+3y=5 because it is given]
=5(4x²-6xy+9y²)
=5(4x²-6*2+9y²).
[6xy =6*2 because it is given that xy=2]
=5(4x²-12+9y²)
=5[(2x)²-2*2x*3y+(3y)²].
[since (a-b)²=a²-2ab+b²]
=5(2x+3y)². [2x+3y=5 given]
=5*(5)²
=5*25
=125
Hope it helps
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