Question

If H.C.F. of 135x² and 189x³ is 108, then find the value of x.

Answer 1

Given:

H.C.F. of 135x² and 189x³ is 108.

Prime factorization:

135 = 3³ × 5

189 = 3³ × 7

H.C.F. of 135 and 189 = 3³ = 27

H.C.F. of x² and x³ = x²

Total H.C.F. = 27x²

According to question:

27x² = 108

`x^2 = 108/27`

x² = 4

x = ±2