Question 1196478
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Left side expression is the sum of four addends.


Three of these addends are monomials of even degree of variable x 
with positive coefficients - so these addends are non-negative at any real value 
of the variable x.


The fourth addend is positive constant "6".


The sum of three non-negative values and fourth positive value can not be equal to zero - 

THEREFORE, left side of the equation can not be zero at any value of x.


So, the equation has no real solutions.
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At this point, the proof is complete.