The HCF of two expressions is x and their LCM is x3 – 9x. If one o

1.	The HCF of two expressions is x and their LCM is x3 – 9x. If one of the expressions is x2 + 3x, then find the other expression.
Answer» HCF = x, LCM = x³ - 9x = x(x² - 9) = x(x + 3)(x - 3) Given expression = x² + 3x = x(x + 3) ∴ Other expression = \(\frac{\text{HCF X LCM}}{\text{Given expression}}\) = \(\frac{x\times{x}\times(x+3)\times(x-3)}{x\times(x+3)}\) = x(x - 3) = x² - 3x

The HCF of two expressions is x and their LCM is x3 – 9x. If one of the expressions is x2 + 3x, then find the other expression.

Answer»

HCF = x,

LCM = x³ - 9x = x(x² - 9) = x(x + 3)(x - 3)

Given expression = x² + 3x = x(x + 3)

∴ Other expression = \(\frac{\text{HCF X LCM}}{\text{Given expression}}\)

= \(\frac{x\times{x}\times(x+3)\times(x-3)}{x\times(x+3)}\)

= x(x - 3) = x² - 3x