Solve the equation f(x)= 54(x-5/3)^3 - 16=0
Could you please explain the method in solving this equation step by step.
Thanks.
2006-12-09 22:43:30 · 4 answers · asked by SHIBZ 2 in Science & Mathematics ➔ Mathematics
add 16 to both sides
54(x-5/3)^3 =16
divide by 54
(x-5/3)^3 =16/54=8/27
(x-5/3)^3 =(2/3)^3
take cube root of both sides
x-5/3 =2/3
add 5/3 to both sides
x=2/3+5/3
x=7/3
2006-12-09 23:01:59 · answer #1 · answered by iyiogrenci 6 · 0⤊ 0⤋
54(x - 5/3)^3 - 16 = 0, so 54(x - 5/3)^3 = 16 (adding 16 to both sides)
and so (x - 5/3)^3 = 16 / 54 = 8 / 27 (dividing both sides by 54).
Take the cube root of both sides and get x - 5/3 = 2/3 (since 2^3 = 8 and 3^3 = 27).
Now add 5/3 to both sides and you have x = 2/3 + 5/3 = 7/3
2006-12-10 07:02:11 · answer #2 · answered by wild_turkey_willie 5 · 0⤊ 0⤋
Since, (x-5/3)^3 = [(3x-5)/3]^3
= (3x-5)^3 / 3^3
= (3x-5)^3 / 27
We have,
54(x-5/3)^3 - 16 = 0
(54/27) (3x-5)^3 - 16 = 0
2 (3x-5)^3 = 16
(3x-5)^3 = 8
3x - 5 = 2 [cube root of both sides]
The solution is left for you.
2006-12-10 06:56:31 · answer #3 · answered by S. B. 6 · 1⤊ 0⤋
54(x-5/3)^3 - 16 = 0
54(x-5/3)^3 = 16
(x-5/3)^3 = 16/54
(x-5/3)^3 = 8/27
x-5/3 = cube root (8/27)
x-5/3 = 2/3
x = 2/3 + 5/3
x = 7/3
x = 2 1/3
2006-12-10 10:27:47 · answer #4 · answered by Kemmy 6 · 0⤊ 0⤋