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The no. Of distinct real solution of equationx2-x-6=x+2

The no. Of distinct real solution of equationx2-x-6=x+2

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1 Answers

Arun
25750 Points
5 years ago
Dear student
 
When openings modulus sign, there are two cases-
If x² -x - 6 is negative
Hence x belongs to [3, -2]
x² - x- 6 = -x -2
x² = 4
x = ±2
Hence +2 and -2, both are accepted
Now
If x² - x- 6 is positive
Hence
X belongs to ( - infinity, -2] U [3, infinity) 
x² - x- 6 = x+ 2
x² - 2x -8 = 0
(x-4) (x+2) = 0
Hence x = -2 and 4 are accepted also
But different soltuisol are 3 i.e. x = 2, -2, 4

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