Respuesta :
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,[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 possible
Case-2:
Let's assume power to 2 is 2
so,[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 possible
Case-3:
Let's assume power to 2 is 3
so,[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 possible
Case-4:
Let's assume power to 2 is 4
so,[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 possible
Case-5:
Let's assume power to 2 is 5
so,[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 possible
Case-6:
Let's assume power to 2 is 6
so,[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 possible
Case-7:
Let's assume power to 2 is 7
so,[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 possible
so, we can write as
[tex]155=2^7+3^3[/tex]................Answer
The 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 will solve it by using the trial and error method.
What is the trial and error method?
Trial and error refers to the process of verifying that a certain choice is right (or wrong)
Case-1:
Let's assume the power to 2 is 1.
so,[tex]2^1+x^3=155[/tex]
now, we can solve for x.
[tex]x^3=155-2[/tex]
[tex]x^3=153[/tex]
it's a cube root not be a number.
So, this is not possible.
Case-2:
Let's assume the power to 2 is 2
[tex]2^2+x^3=155\\4+x^3=155\\x^3=155-4\\x^3=151[/tex]
again it's cube root not be a number
so, this is not possible
Case-3:
Let's assume the power to 2 is 3
[tex]2^3+x^3=155\\8+x^3=155\\x^3=155-8\\x^3=147[/tex]
it's a cube root not be a number
so, this is not possible
Case-4:
Let's assume the power to 2 is 4
[tex]2^4+x^3=155\\x^3=155-16\\x^3=139[/tex]
again it's cube root not be a number
so, this is not possible
Case-5:
Let's assume the power to 2 is 5
[tex]2^5+x^3=155\\x=123[/tex]
again it's cube root not be a number
so, this is not possible
Case-6:
Let's assume the power to 2 is 6
[tex]2^6+x^3=155\\x^3=91[/tex]
again it's cube root not be a number
so, this is not possible
Case-7:
Let's assume the power to 2 is 7
[tex]2^7+x^3=155[/tex]
[tex]x^3=27[/tex]
its cube root will be 3
This is a possible case
Therefore, we can write as,
[tex]155=2^7+3^3[/tex]
To learn more about the trial and error method visit:
https://brainly.com/question/25878205
