Home
Class 12
MATHS
If 3x^(2)-2ax+(a^(2)+2b^(2)+2c^(2))=2(ab...

If `3x^(2)-2ax+(a^(2)+2b^(2)+2c^(2))=2(ab+bc)`, then `a`, `b`, `c` can be in

A

`A.P.`

B

`G.P.`

C

`H.P.`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` The given result can be written as
`{x-(a-b)^(2)}+{x-(b-c)^(2)}+(x-c)^(2)=0`
`impliesx=a-b` `x=b-c` `x=c`
`a-b=b-c=c`
From `a-b=b-c`, `2b=a+c`
`:.a,b,c` can be in `A.P.`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Examples|120 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.1|3 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE|Exercise NUMARICAL VALUE TYPE|2 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

If a+b+c=4 and a^(2)+b^(2)+c^(2)+3(ab+bc+ac)=21 where a, b, c in R then ab+bc+ca=

Knowledge Check

  • If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca) , than a,b,c are in

    A
    AP only
    B
    GP only
    C
    GP and AP
    D
    None of these

  • If quadratic equation ax^(2) + bx + ab + bc + ca - a^(2) - b^(2) - c^(2) = 0 where a, b, c distinct reals, has imaginary roots than (A) a+b+ab+bc+calta^(2)+b^(2)+c^(2) (B) a-b+ab+bc+cagta^(2)+b^(2)+c^(2) (C) 4a+2b+ab+bc+calta^(2)+b^(2)+c^(2) (D) 2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0

    A
    `a+b+ab+bc+calta^(2)+b^(2)+c^(2)`
    B
    `a-b+ab+bc+cagta^(2)+b^(2)+c^(2)`
    C
    `4a+2b+ab+bc+calta^(2)+b^(2)+c^(2)`
    D
    `2(a+-3b)-9{(a-b)^(2)+(b-c)^(2)+(c-a)^(2)}lt0`

  • Suppose A, B, C are defined as A = a^(2)b + ab^(2) - a^(2)c - ac^(2), B = b^(2)c + bc^(2) - a^(2)b - ab^(2) , and C = a^(2)c + ac^(2) - b^(2)c - bc^(2) , where a gt b gt c gt 0 and the equation Ax^(2) + Bx + C = 0 has equal roots, then a, b, c are in

    A
    A.P.
    B
    G.P.
    C
    H.P.
    D
    A.G.P.

    • Similar Questions

    Explore conceptually related problems

    If a,b,c in R and a^(2)+(5)/(2)b^(2)+c^(2)=2ab+bc+ca, then then a+2b+2c may be

    If a^(2) +b^(2) +c^(2) = ab + bc + ca then (a+b)/(c ) + (b+c)/(a) + (c+a)/(b) =?

    If a^(2) +b^(2) +c^(2) = ab + bc + ca then (c )/(a+b) + (b)/(a +c)+ (c )/(a+b) = ?

    If x=a^(2) - bc, y=b^(2) - ca, z=c^(2) - ab then what is the value of (ax+by+ cz)/( (a+b+c) (x+y+z) )

    If (a ^(2) - b c)/( a ^(2 ) + bc)+ (b ^(2) -ca)/( b ^(2) + ca) + (c ^(2) - ab)/( c ^(2) + ab) =1, then the value of (a ^(2))/(a ^(2) + bc ) + (b ^(2))/(b ^(2) + ac) + (c ^(2))/( c ^(2) + ab) is

    Home
    Profile