Proving Nonnegativity of 3 Numbers with Crazy Exponents | Nonconstructive Proof

[n00neimp0rtnt]

Homework Statement

I barely even know where to begin with this proof:

Show that the product of two of the numbers 65¹⁰⁰⁰ - 8²⁰⁰¹ + 3¹⁷⁷, 79¹²¹² - 9²³⁹⁹ + 2²⁰⁰¹ and 24⁴⁴⁹³ - 5⁸¹⁹² + 7¹⁷⁷⁷ is nonnegative.

I also have to state if it is constructive or nonconstructive, and I'm not supposed to evaluate the numbers.

Homework Equations

The Attempt at a Solution

The most I can come up with so far is that the proof is likely "nonconstructive" since I am not out to find a single element to make the statement true; I have to determine it in another fashion.

 

[DaveC426913]

Homework Statement

I barely even know where to begin with this proof:

Show that the product of two of the numbers 65¹⁰⁰⁰ - 8²⁰⁰¹ + 79¹²¹² - 9²³⁹⁹ + ²⁰⁰¹ and 24⁴⁴⁹³ - 5⁸¹⁹² + 7¹⁷⁷⁷ is nonnegative.

I also have to state if it is constructive or nonconstructive, and I'm not supposed to evaluate the numbers.

Homework Equations

The Attempt at a Solution

The most I can come up with so far is that the proof is likely "nonconstructive" since I am not out to find a single element to make the statement true; I have to determine it in another fashion.

Well, I have not studied this so please take my suggestion with a grain of salt but: it seems to me that, according to the law of exponents, you can add exponents to arrive at a value (1000-2001+1212-2399 = -187). When you do this, both numbers have a negative value (though we do not know the magnitude), which means the product will have to be positive.

 

[n00neimp0rtnt]

I have revised the equation. Can anyone assist me?