Solve and suggest level of the problem,i have marked it as level 4

Algebra Level 3

find out the sum of all integral roots of the equation 3 − x − x + 1 > 1 2 \sqrt{3-x}-\sqrt{x+1}>\frac{1}{2}

this question is not purely mine


The answer is -1.

Atul Shivam by Atul Shivam , 23, India

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1 solution

Pulkit Gupta
Nov 19, 2015

The domain of the function is [-1,3]. Since the values are few, we substitute the values into the equation and find the values of x for which the equality satisfies.

P.S. I shall suggest Level 3. The problem is very easy if the solver knows the approach.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

but @Pulkit Gupta , when i solved using the basic method of squaring two times i got quadratic equation whose solution was x<1-(sqrt(7)/4) and x>1+(sqrt(7)/4). yes the domain is [-1,3]. but then the integral solutions would be -1,0,2,3. hence i got ans. as 4

A Former Brilliant Member - 2 years, 10 months ago

yes me too.

Mrunang Kothari - 1 year, 10 months ago

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