perplexus.info :: Just Math : What base?

What base? (Posted on 2022-05-28)

What base will make the bold text true: Equation: 3x²-25x+66=0
It’s solutions x₁=4 and x₂=9 ?

Provide your reasoning.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Same solution, different approach

| Comment 2 of 3 |

In any base (10 or greater), the equation must be 3(x-4)(x-9) = 0

Expanding (in base 10) gives 3x^2 - 39x + 108 = 0

Then then 2*base + 5 = 39, so base = 17.

This checks, as 6*17+ 6 = 108

Edited on May 28, 2022, 4:08 pm

Posted by Steve Herman on 2022-05-28 08:48:06

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