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can you simplify this sum the final
answer will really blow your mind also
you cannot use a calculator let us call
this value as a and this as B which is
square root conjugate of a both the cube
root of a and the cube root of B are
real therefore their sum will also be
real write this as the cube root of a
plus the cube root of B and let us call
this sum as X
now Cube both sides to get this we know
that the A + B whole cube is given by
this formula so X Cube will be equal to
this Cube or a plus this plus this plus
this Cube or B first put these squares
inside of this cube root and then we
will group these cube roots together
here comes the magic write this as a a
and b sare as BB oh look
we have AB as common here and what will
be the value of its product it will be 7
2us < tk50 s or 49 - 50 or -1 we can
rewrite this Min -1 as -1 Cub now
substitute that here and now if we take
the cube root of the negative 1 we get a
negative one here so this will become a
+ b minus 3 * this plus this amazing
now this sum is same as X and therefore
we have X Cub = a + b - 3 * X now A and
B are conjugates of each other and
therefore their sum will be 7 + < tk50 +
7 - < tk50 this will be cancelled and we
are left with 14 thus we have this cubic
equation and now we just have to solve
for this and we are done take this 3 X
on left hand side to get X Cub + 3x = 14
now we can write 14 as 8 + 6 or 8 + 3 *
2 so compare both sides to get one of
the solutions to this equation as x = 2
after that we can Factor this equation
to get x - 2 * this quadratic equation
the roots of this quadratic equation are
imaginary therefore the only real value
of sum is two wow did you expect such a
complicated sum to turn out as an
integer isn't this cool if you like it
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