Question

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

Answer 1

Answer : $\bold{2^7 + 3^3 \: = \: 155}$


Explanation -

Given that 155 can be expressed as the sum of a power of 2 and a cube Numbers

Let the power of 2 is 7.

According to the given question -

${2}^{7} + {x}^{3} = 155$

Solve x -

${2}^{7} + {x}^{3} = 155$

$128 + {x}^{3} = 155$

${x}^{3} = 155 - 128$

${x}^{3} = 27$

$x = {3}^{3}$

So, 128 + 27 = 155


Hence :

$\bold{Answer : 2^7 + 3^3 \: = \: 155}$

Answer 2

Answer:

2⁷ + 3³

Step-by-step explanation:

We know that one of the number is 2ⁿ

Therefore, we try:

155 - 2¹ = 153 (But ∛153 ≠ integer)

155 - 2² = 151 (But ∛151 ≠ integer)

155 - 2³ = 147 (But ∛147 ≠ integer)

155 - 2⁴ = 139 (But ∛139 ≠ integer)

155 - 2⁵ = 123 (But ∛123 ≠ integer)

155 - 2⁶ = 91 (But ∛92 ≠ integer)

155 - 2⁷ = 27(∛27 ≠ 3)

So the answer is 2⁷ + 3³

Answer: 2⁷ + 3³