1.

[x+5]²=[x+6]+5, where[.] denotes the greatest integer function

Answer»
{x}^{2}  + 25 + 10x = x + 11
{x}^{2}  + 9x + 14 = 0
by splitting the middle term.
{x}^{2}  + 2x + 7x + 14 = 0
x(x + 2) + 7(x + 2)
(x + 2)(x + 7) = 0
x=either -7or -2


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