LCM and GCD Solution3





In this page lcm and gcd solution3 we are going to see solution of some questions with detailed explanation.

(iii) (x⁴ - y⁴) (x⁴ + x²y² + y⁴) , x² - y² , x⁴ - y⁴

Solution:

 L.C.M x G.C.D = p (x) x q (x)

 L.C.M = (x⁴ - y⁴) (x⁴ + x²y² + y⁴)

 G.C.D = x² - y²

 p (x) = x⁴ - y⁴

  q (x) = [ L.C.M G.C.D ]/p (x)

         = [ (x⁴ - y⁴) (x⁴ + x²y² + y⁴) (x² - y²)]/(x⁴ - y⁴)

  q (x) = (x⁴ + x²y² + y⁴) (x² - y²)


(iv) (x³ - 4 x) (5 x + 1) , (5 x² + x) , (5 x³ - 9 x² - 2x)

Solution:

 L.C.M x G.C.D = p (x) x q (x)

 L.C.M = (x³ - 4 x) (5 x + 1)

 G.C.D = (5 x² + x)

 p (x) = (5 x³ - 9 x² - 2x)

  q (x) = [ L.C.M G.C.D ]/p (x)

         = [ (x³ - 4 x) (5 x + 1) (5 x² + x)]/(5 x³ - 9 x² - 2x)

         = [ x (x² - 4) (5 x + 1)  x (5 x + 1)]/ x (5 x² - 9 x - 2)

         = [ x² (x + 2) (x - 2) (5 x + 1) (5 x + 1)]/ x (5 x + 1) (x - 2)

 q (x) = x (x + 2) (5 x + 1)  


(v) (x - 1) (x - 2) (x² - 3 x + 3) , (x - 1) , (x³ - 4 x² + 6 x - 3)

Solution:

 L.C.M x G.C.D = p (x) x q (x)

 L.C.M = (x - 1) (x - 2) (x² - 3 x + 3)

 G.C.D = (x - 1)

 p (x) = (x³ - 4 x² + 6 x - 3)

  q (x) = [ L.C.M G.C.D ]/p (x)

         = [ (x - 1) (x - 2) (x² - 3 x + 3) (x - 1)]/(x³ - 4 x² + 6 x - 3)

let us use synthetic division to find factors of the cubic equation.

         = [ (x - 1) (x - 2) (x² - 3 x + 3) (x - 1)]/(x - 1) (x² - 3 x + 3)

         = (x - 2) (x - 1)


(vi) 2 (x + 1) (x² - 4) , (x + 1), (x + 1) (x - 2)

Solution:

 L.C.M x G.C.D = p (x) x q (x)

 L.C.M = 2 (x + 1) (x² - 4)

 G.C.D = (x + 1)

 p (x) = (x + 1) (x - 2)

  q (x) = [ L.C.M G.C.D ]/p (x)

         = [ 2 (x + 1) (x² - 4) (x + 1) ]/(x + 1) (x - 2)

         = [ 2 (x + 1) (x + 2) (x - 2) (x + 1) ]/(x + 1) (x - 2)

   q (x) = 2 (x + 1) (x + 2)

lcm and gcd solution3 lcm and gcd solution3