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Solve the following equation 22r1 - \(\frac{...

Solve the following equation 22r1 - 53 = 1r+2

A.

(52, 1)

B.

(5, -4)

C.

(2, 1)

D.

(1, 52)

E.

(1,-2)

Correct answer is D

22r1 - 53 = 1r+2

22r1 - 1r+2 = 53

2r+42r+12r1(r+2) = 53

5(2r+1)(r+2) = 53

5(2r - 1)(r + 2) = 15

(10r - 5)(r + 2) = 15

10r2 + 20r - 5r - 10 = 15

10r2 + 15r = 25

10r2 + 15r - 25 = 0

2r2 + 3r - 5 = 0

(2r2 + 5r)(2r + 5) = r(2r + 5) - 1(2r + 5)

(r - 1)(2r + 5) = 0

r = 1 or 52