(20x+22)^1/3 - (20x-22)^1/3 = 2
Cube both sides
[(20x+22)^1/3 - (20x-22)^1/3]^3 = 8
(20x+22) - (20x-22) - 3(20x+22)^1/3(20x-22)^1/3[(20x+22)^1/3 - (20x-22)^1/3] = 8
Original equation appears in result, so substitute a 2.
44 - 6(20x+22)^1/3(20x-22)^1/3 = 8
6(20x+22)^1/3(20x-22)^1/3 = 36
(20x+22)^1/3(20x-22)^1/3 = 6
(20x+22)*(20x-22) = 6^3 = 216
400x^2 - 484 = 216
400x^2 = 700
x^2 = 7/4
x = ±√7/2 but we are constrained to a positive value so
x = √7/2
(and besides, using x = -√7/2 does not solve the original equation)
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Posted by Larry
on 2024-10-27 15:17:05 |
Solution