Question

If 4x+ 1/5=2, then 125x^3+1/643 is

Answer 1

125x3-1=0

Three solutions were found :

x =(-5-√-75)/50=(-1-i√ 3 )/10= -0.1000-0.1732i

x =(-5+√-75)/50=(-1+i√ 3 )/10= -0.1000+0.1732i

x = 1/5 = 0.200

Step by step solution :

Step 1 :

Equation at the end of step 1 :

53x3 - 1 = 0

Step 2 :

Trying to factor as a Difference of Cubes:

2.1 Factoring: 125x3-1

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3