without actually calculating the cubes find the value of (1/2)cube+(1/3)cube-(5/6)cube
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Q. (1/2)^3 + (1/3)^3 - (5/6)^3
we know, -(5/6) can be written as +(-5/6)
applying x^3+y^3+z^3-3xyz
put x=1/2, y=1/3, z=5/6
if x+y+z=0
x^3+y^3+z^3-3xyz=0
x^3+y^3+z^3=3xyz
therefore, (1/2)^3 +(1/3)^3+(-5/6)^3 =
3×1/2×1/3×(-5/6)
--->1/2×-5/6
we get, the answer as -5/12.
Hope this helps. :)
we know, -(5/6) can be written as +(-5/6)
applying x^3+y^3+z^3-3xyz
put x=1/2, y=1/3, z=5/6
if x+y+z=0
x^3+y^3+z^3-3xyz=0
x^3+y^3+z^3=3xyz
therefore, (1/2)^3 +(1/3)^3+(-5/6)^3 =
3×1/2×1/3×(-5/6)
--->1/2×-5/6
we get, the answer as -5/12.
Hope this helps. :)
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