ICSE Class 10CISCE
Share
Notifications

View all notifications

If X = (M + 1) + (M + 1)/(M + 1) - (M - 1) Then Prove that X3 - 3mx2 + 3x = M - ICSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

If x = `(root (3)("m + 1") + root (3)("m - 1"))/(root (3)("m + 1") + root (3)("m - 1")` then prove that x3 - 3mx2 + 3x = m

Solution

`"x"/1 = (root (3)("m + 1") + root (3)("m - 1"))/(root (3)("m + 1") + root (3)("m - 1")`

Applying componendo and dividendo 

`("x"+ 1) /("x" - 1) = (root (3)("m + 1") + root (3)("m - 1") + root (3)("m + 1") - root (3)("m - 1"))/ (root (3)("m + 1") + root (3)("m - 1") - root (3)("m + 1") + root (3)("m - 1")`

`=> ("x"+ 1) /("x" - 1) = (2 root (3)("m" + 1))/(2 root (3)("m" - 1))`

Cubing both sides 

`=> ("x" + 1)^3/("x - 1")^3 = (8 ("m + 1"))/(8("m - 1"))`

`=> ("x"^3 + 3"x"^2 +3"x" +1)/("x"^3 - 3"x"^2 + 3"x" -1) = ("m + 1")/("m - 1")`

⇒  (m - 1) (x3 + 3x2 + 3x + 1) = (m + 1 )(x3 - 3x2 + 3x - 1) 

⇒ mx3 + 3mx2 + 3mx + m - x3 - 3x2 - 3x - 1 - mx3 - 3mx2 + 3mx - m + x3 - 3x2 + 3x -1

⇒ 6mx2 + 2m - 2x3 - 6x = 0 

⇒ 3mx2+ m - x3 - 3x  = O 

⇒  x3 - 3mx2 + 3x = m 

Hence Proved.

  Is there an error in this question or solution?

APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 13

Video TutorialsVIEW ALL [1]

Solution If X = (M + 1) + (M + 1)/(M + 1) - (M - 1) Then Prove that X3 - 3mx2 + 3x = M Concept: Componendo and Dividendo Properties.
S
View in app×