If 2x+3y=12 and xy=6, find the value of 8 x + 27 . 3 y
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Answer:
2x+3y=12 xy=6
8x
3
+27y
3
=(2x)
3
+(3y)
3
=a
3
+b
3
=(a+b)(a
2
+b
2
−ab)
8x
3
+27y
3
=(2x+3y)((2x)
2
+(3y)
2
−(2x)(3y))
=(12)[(2+3y)
2
−12xy−6xy]
=(12)[(12)
2
−18(6)]
=12[144−108]
=12×36
=432.2x+3y=12 xy=6
8x
3
+27y
3
=(2x)
3
+(3y)
3
=a
3
+b
3
=(a+b)(a
2
+b
2
−ab)
8x
3
+27y
3
=(2x+3y)((2x)
2
+(3y)
2
−(2x)(3y))
=(12)[(2+3y)
2
−12xy−6xy]
=(12)[(12)
2
−18(6)]
=12[144−108]
=12×36
=432.
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