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Find the solution of the equation: √(x^2-16)-(x-4)=√(x^2-5x+4)

Find the solution of the equation: √(x^2-16)-(x-4)=√(x^2-5x+4)

Grade:10

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
sqrt (x- 4) is common in each term hence x = 4 can be. solution. aprt from this
 
sqrt(x + 4) – sqrt (x- 4) = sqrt (x- 1)
 
x = 5 is also a solution.
 
x +4 = x – 4 + x – 1 + 2 sqrt (x^2 – 5x + 4)
 
x^2 +81 – 18 x = 4 x^2 —20 x + 16
 
3 x^2 – 2 x – 65 = 0
 
by solving quadratic equation
 
x = 5 and -26/6
 
here – 26/6 is rejected as not satisfied in original equation

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