Home
Class 12
MATHS
Let a, b, c ne three distinct non-zero r...

Let `a`, `b`, `c` ne three distinct non-zero real numbers satisfying the system of equation `(1)/(a)+(1)/(a-1)+(1)/(a-2)=1` , `1/b+(1)/(b-1)+(1)/(b-2)=1` , `(1)/(c )+(1)/(c-1)+(1)/(c-2)=1`. Then `abc=` (a) 1 (b)2 (c)3 (d)4

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `a`, `b`, `c` are roots of equation `(1)/(x)+(1)/(x-1)+(1)/(x-2)=1`
`implies(x-1)(x-2)+x(x-2)+x(x-1)=x(x-1)(x-2)`
`impliesx^(3)-6x^(2)+8x-2=0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are three distinct positive real numbers, then the least value of ((1+a+a^(2))(1+b+b^(2))(1+c+c^(2)))/(abc) , is

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

If a, b, c are distinct positive real numbers such that a+(1)/(b)=4,b+(1)/( c )=1,c+(1)/(d)=4 and d+(1)/(a)=1 , then

If a, b,c are three positive real numbers , then find minimum value of (a^(2)+1)/(b+c)+(b^(2)+1)/(c+a)+(c^(2)+1)/(a+b)

If a, b, c are positive real numbers, then the least value of (a+b+c)((1)/(a)+(1)/(b)+(1)/( c )) , is

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove that ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

If a, b, c are positive real numbers such that a+b+c=1 , then the greatest value of (1-a)(1-b)(1-c), is

If a,b,c are non-zero real numbers, then the minimum value of the expression ((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2)) equals

Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a=(1-b^3)/b=(1-c^3)/c dot The value of (a^3+b^3+c^3) is _____________.