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Algebra Level 4

$\large\frac{1-\sqrt{x^2+x-2}}{x-1}\leq 1$ How many integer values of $x$ don't satisfy the inequality above?

0 1 2 3 More than 3 (countable) Infinitely many

1 solution

A Former Brilliant Member
May 6, 2017

-1,0 and 1 do not satisfy. Verify and select the correct answer.

But at -1,0.....the expression under the square root is negative....and the entire expression is undefined at x=1. So these values should not be taken into consideration. So satisfying or not satisfying the inequality is out of question. Think about it.....at x=1 the expression itself is undefined....so how can we be certain that it does notsatisfy an inequality. Or for the other values...the valuepf the expression becomes complex.... And we know that the field of complex number is not ordered....so how can we say anything about the inequality

Arghyadeep Chatterjee - 1 year, 7 months ago

all negative numbers. All positive numbers. 0. none of these work. no integers.

Odin Wang - 10 months ago

exactly the answer should be none @Odin Wang

Arghyadeep Chatterjee - 10 months ago

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