Maths Question???

Question

Solve this equation without using calculator:
(12x-1)*(6x-1)*(4x-1)*(3x-1)=5

Answer 1

Ok, here you just need to operate like this :

(12x -1)*(6x-1)*(4x-1)*(3x-1) =5

[72x^2 - 12x - 6x + 1]*[12x^2 - 4x -3x + 1] = 5

[72x^2 - 18x + 1]*[12x^2 - 7x + 1] = 5

72*12 = 6*12*6*2 = 864

then :

864x^4 - 504x^3 + 72x^2 - 216x^3 + 126x^2 - 18x + 12x^2 - 7x +1 = 5

864x^4 - 720x^3 + 210x^2 - 25x - 4 = 0

A value for x = 1/2, you can find them aplying ruffinis law.

Well, that's the equation, and a value will be x =1/2

Another value will be, 3/2, you can replace it, and you will find out that fits on the equation, another one that i've found is 2.

Answer 2

One of the four numbers is 5 & the others are 1.
check which one can be 1.
12x-1=1 12x=2 x=1/6 if x=1/6 then 6x-1=0
6x-1=1 6x=2 x=1/3 if x=1/3 then 3x-1=0
4x-1=1 4x=2 x=1/2
the answer is 1/2.
(12*1/2-1)(6*1/2-1)(4*1/2-1)(3*1/2-1)=(6-1)(3-1)(2-1)(3/2-1)=5*2*1*1/2=5
Good Luck

Answer 3

first,
(12x-1)*(6x-1)*(4x-1)*(3x-1)=5
=>x= 1/2 or 1 or 3/2 or 2
because
12x-1=5=>x=1/2
6x-1=5=>x=1
4x-1=5=>x=3/2
3x-1=5=>x=2.