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

we are given

a number as 155

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

we can solve it by using trial and error method

Case-1:

Let's assume power to 2 is 1

so,

now, we can solve for x

it's cube root won't be a number

so, this is not possible

Case-2:

Let's assume power to 2 is 2

so,

now, we can solve for x

it's cube root won't be a number

so, this is not possible

Case-3:

Let's assume power to 2 is 3

so,

now, we can solve for x

it's cube root won't be a number

so, this is not possible

Case-4:

Let's assume power to 2 is 4

so,

now, we can solve for x

it's cube root won't be a number

so, this is not possible

Case-5:

Let's assume power to 2 is 5

so,

now, we can solve for x

it's cube root won't be a number

so, this is not possible

Case-6:

Let's assume power to 2 is 6

so,

now, we can solve for x

it's cube root won't be a number

so, this is not possible

Case-7:

Let's assume power to 2 is 7

so,

now, we can solve for x

it's cube root will  be 3

so, this is  possible

so, we can write as

................Answer