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MATH / The largest value of x that satisfies √(x+1)=x can be written as (a+√(b))/(c) where c has no common factor with a and √(b) and b is not divisible by the square of any integer great…

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problem

The largest value of xx that satisfies x+1=x\sqrt{x+1}=x can be written as a+bc\dfrac{a+\sqrt{b}}{c} where cc has no common factor with aa and b\sqrt{b} and bb is not divisible by the square of any integer greater than 1. What is the value of a+b+ca+b+c?
Plain-text mathematical notation (without MathML)
The largest value of x that satisfies √(x+1)=x can be written as (a+√(b))/(c) where c has no common factor with a and √(b) and b is not divisible by the square of any integer greater than 1. What is the value of a+b+c?
Original LaTeX notation
The largest value of $x$ that satisfies $\sqrt{x+1}=x$ can be written as $\dfrac{a+\sqrt{b}}{c}$ where $c$ has no common factor with $a$ and $\sqrt{b}$ and $b$ is not divisible by the square of any integer greater than 1. What is the value of $a+b+c$?

level

Level 4

type

Algebra

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Source and history

task_id
75e21850-56d3-5d16-868c-a236c13feb49
task_key
algebra--test--75e21850-56d3-5d16-868c-a236c13feb49
task_revision_id
1
config / split
algebra / test

Official source

initial import