# Tricky maths question. Find base of equation given solutions.

• tigertan
In summary, the conversation involved solving for the base of an unknown number system using two equations. By comparing coefficients and setting them equal to each other, it was determined that the base must be greater than 8 and equal to 13. This was confirmed by checking the middle term of the equations and obtaining the same result.
tigertan

## Homework Statement

5x2-50x+125 (equation 1)
Solutions are x=5 and x=8

(x-5)(x-8)
= x2-13x+40 (equation 2)

What is the base of the number system??

## The Attempt at a Solution

Compare coefficients
1a=5b
-13a=-50b
40a=125b

The base must be greater than 8 since 8 is the highest solution..

Descriminant of (1) is zero. Only one solution

Last edited:
tigertan said:
Compare coefficients
1a=5b
I don't understand what you're doing there. What are a and b?
How about taking the base to be a and writing out exactly what the equations mean in those terms, e.g. '125' becomes a2+2a+5.

Saying 1=5 in any bases is nonsensical. The form of your equation must be C*(x-5)*(x-8) in any base. Doesn't that tell you what C must be?

Last edited:
Dick said:
Saying 1=5 in any bases is nonsensical. The form of your equation must be C*(x-5)*(x-8) in any base. Doesn't that tell you what C must be?

Yess whoops c=5

tigertan said:
Yess whoops c=5

Ok, so work it out in base 10 then equate it to the unknown base in (equation 1).

Still not sure how I'm meant to solve for the base?!

tigertan said:
Still not sure how I'm meant to solve for the base?!

What's 5*(x-8)*(x-5) in base 10? The value of this expression doesn't depend on the base.

okay shall give it a go!

tigertan said:
okay shall give it a go!

Try and stay on the forums instead of using private messaging. If you tell me why it's base 13, I'll probably tell you it's correct.

Last edited:
looking only at the middle term, -50x of equation with unknown base, equating -5a=-65, we obtain a=13

tigertan said:
looking only at the middle term, -50x of equation with unknown base, equating -5a=-65, we obtain a=13

That's correct. You can check it by showing you get the same result from the last term.

## 1. How do I approach a tricky math question?

The best way to approach a tricky math question is to break it down into smaller, more manageable steps. Identify what information you have been given and what you need to find. Then, use any relevant formulas or equations to help you solve the problem. Don't be afraid to try different approaches or ask for help if you get stuck.

## 2. What is a base in an equation?

In math, a base is the number or expression that is being raised to a power. For example, in the equation 23, the base is 2. The power, 3, tells us how many times to multiply the base by itself.

## 3. What are solutions in a math problem?

Solutions in a math problem refer to the values that make the equation or inequality true. In other words, it is the value that satisfies the equation or inequality. For example, in the equation 3x + 5 = 20, the solution is x = 5 because when we substitute 5 for x, the equation becomes 3(5) + 5 = 20, which is true.

## 4. How do I find the base of an equation given solutions?

To find the base of an equation given solutions, you need to use the inverse operation of the exponent. For example, if the solution to an equation is 8 and the exponent is 2, then the base is the square root of 8, which is 2. If the solution is 27 and the exponent is 3, then the base is the cube root of 27, which is 3.

## 5. Can I use a calculator to solve a tricky math problem?

It depends on the specific problem and the instructions given. Some math problems may require you to use a calculator, while others may need to be solved without one. It's important to read the instructions carefully and follow any given guidelines. That being said, using a calculator can be helpful in checking your work and saving time, but it's important to understand the concepts behind the problem as well.

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