Question

solve to find the zeroes (roots) of the following equation

x⅔+x⅓-2=0

(kindly do not answer if you don't know the answer) ​

Answer 1

Answer:

(-7 ± √17)/2

Step-by-step explanation:

x⅔ + x⅓ - 2 = 0

x⅔ + x⅓ = 2. (1)

Take cube both sides

(x⅔ + x⅓)³ = 2³ = 8

Use formula (a+b)³ = a³ + b³ + 3ab(a+b)

x² + x + 3*x⅔*x⅓*(x⅔ + x⅓) = 8

From (1) put value x⅔ + x⅓ = 2

Also simplify the term x⅔*x⅓ = x¹ (as you know when multiplying same variables their powers add up)

thus equation becomes

x² + x +3x*2 = 8

x² + 7x - 8 = 0

Now this is a quadratic equation which we can solve

Roots of this equation are

x = {-7 ± √(49-32)} / 2 = (-7 ± √17)/2