13 Solve 2r 14 Solve 0 r 5 ar2 SolutionA 2x 423x2 0 2x 43

13. Solve 2r 14. Solve 0 (r +5) ar-2

Solution

A.

2x - 423/x^2 = 0

2x = 432/x^2

x*x^2 = 432/2

x^3 = 216

x = (216)^(1/3)

x = 6

B.

[(x + 5)^2*(x - 2) - (x - 2)^2]/(x + 5)^2 = 0

[(x + 5)^2*(x - 2) - (x - 2)^2] = 0

(x - 2)*[(x + 5)^2 - (x - 2)] = 0

(x - 2)*(x^2 + 10x + 25 - x + 2) = 0

(x - 2)*(x^2 + 9x + 27) = 0

(x - 2) = 0

x = 2

OR

(x^2 + 9x + 27) = 0

above equation has no solution, since D < 0

D = b^2 - 4ac = 9^2 - 4*27 < 0

So above equation will have imaginary solution.

Only solution will be x = 2