Question

Ex. 3. What could be the maximum value of Q in the following equation
5P9 + 3R7 + 2Q8 =1114
​

Answer 1

Answer:

96td8d8ttdpourzuorRz0

Answer 2

Step-by-step explanation:

What could be the maximum value of Q in the following equation, 5P9 + 3R7 + 2Q8 = 1114?

I assume you mean: [math]5P^9 + 3R^7 + 2Q^8 = 1114[/math]

Is it really that hard to give some clue that you mean exponentiation?

You have not provided any restrictions as to the values of P, Q or R; that’s good, it makes the question easier!

Let’s start with P = R = -1

We thus have: [math]-5 -3 + 2Q^8 = 1114 \rightarrow Q^8 = 561[/math]

This, of course, leads to 8 values of Q, two of which are real (circa ± 2.206), two are completely ‘imaginary’ (circa ± 2.206i) and the others form two complex conjugate pairings (circa ± 1.56 ± 1.56i). When you are dealing with several complex numbers, how do you determine which is the biggest? You could use the absolute value, but this would be the same for all eight values of Q. I know, I will only consider the real part of each number. This gives Q = 2.206 (to 3 decimal places).

I’m not happy with this; let’s make P = -10, R = 0

We thus have: [math]-5000000000 + 2Q^8 = 1114 \rightarrow Q^8 = 2500000557[/math]

This gives us Q = 14.453 (to 3 dp).

Still not happy; lets make P = -100, R = 0

We thus have: [math]-5000000000000000000 + 2Q^8 = 1114 \rightarrow Q^8 = 2500000000000000557[/math]

This gives us Q = 199.408 (to 3 dp).

By selecting ever smaller values of P (and R), we will obtain ever larger values of Q. Thus, there is no largest value of Q.

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Now, if you had provided restrictions, for example P, Q and R are non-negative, there would be a maximum value of Q. But, that would be answering a question you didn’t ask!