Show that 155 can be expressed as the sum of a power of 2 and a cube number.

we are given a number as 155155 can be expressed as the sum of a power of 2 and a cube numberwe can solve it by using trial and error methodCase-1:Let's assume power to 2 is 1so,[tex]2^1+x^3=155[/tex]now, we can solve for x[tex]x^3=153[/tex]it's cube root won't be a number so, this is not possibleCase-2:Let's assume power to 2 is 2so,[tex]2^2+x^3=155[/tex]now, we can solve for x[tex]x^3=151[/tex]it's cube root won't be a number so, this is not possibleCase-3:Let's assume power to 2 is 3so,[tex]2^3+x^3=155[/tex]now, we can solve for x[tex]x^3=147[/tex]it's cube root won't be a number so, this is not possibleCase-4:Let's assume power to 2 is 4so,[tex]2^4+x^3=155[/tex]now, we can solve for x[tex]x^3=139[/tex]it's cube root won't be a number so, this is not possibleCase-5:Let's assume power to 2 is 5so,[tex]2^5+x^3=155[/tex]now, we can solve for x[tex]x^3=123[/tex]it's cube root won't be a number so, this is not possibleCase-6:Let's assume power to 2 is 6so,[tex]2^6+x^3=155[/tex]now, we can solve for x[tex]x^3=91[/tex]it's cube root won't be a number so, this is not possibleCase-7:Let's assume power to 2 is 7so,[tex]2^7+x^3=155[/tex]now, we can solve for x[tex]x^3=27[/tex]it's cube root will  be 3 so, this is  possibleso, we can write as[tex]155=2^7+3^3[/tex]................Answer