Answer:
The numbers are [tex]-39,-37,-35[/tex]
Step-by-step explanation:
Let
x-----> the first odd number
x+2----> the middle odd number
x+4---> the third odd number
[tex]x(x+2)(x+4)=(x+2)^{3} +148[/tex]
[tex](x^{2}+2x)(x+4)=(x^{2}+4x+4)(x+2)+148\\x^{3}+4x^{2}+2x^{2}+8x=x^{3}+2x^{2}+4x^{2}+8x+4x+8+148\\x^{3}+6x^{2}+8x=x^{3}+6x^{2}+12x+156\\8x=12x+156\\4x=-156\\x=-39[/tex]
The numbers are
[tex]x=-39[/tex]
[tex]x+2=-39+2=-37[/tex]
[tex]x+4=-39+4=-35[/tex]
