Home
Class 12
MATHS
If 4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca),...

If `4a^(2)+9b^(2)+16c^(2)=2(3ab+6bc+4ca)`, where a,b,c are non-zero real numbers, then a,b,c are in GP.
Statement 2 If `(a_(1)-a_(2))^(2)+(a_(2)-a_(3))^(2)+(a_(3)-a_(1))^(2)=0`, then `a_(1)=a_(2)=a_(3),AA a_(1),a_(2),a_(3) in R`.

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1

C

Statement 1 is true, Statement 2 is false

D

Statement 1 is false, Statement 2 is true

Text Solution

Verified by Experts

The correct Answer is:
D
Statement 1 `4a^(2)+9b^(2)+16c^(2)-2(3ab+6bc+4ca)=0`
`implies (2a)^(2)+(3b)^(2)+(4c)^(2)-(2a)(3b)-(3b)(4c)-(2a)(4c)=0`
`implies (1)/(2){(2a-3b)^(2)+(3b-4c)^(2)+(4c-2a)^(2)}=0`
`implies 2a-3b=0" and "3b-4c=0" and "4c-2a=0`
`implies" and " b=(4c)/(3)" and " c=(a)/(2) implies a=(3b)/(2)" and " b=(4c)/(3)" and " c=(3b)/(4)`
Then,a,b,c are of the form `(3b)/(2),b,(3b)/(4)`, which are in HP.
So, Statement 1 is false.
Statement 2 If `(a_(1)-a_(2))^(2)+(a_(2)-a_(3))^(2)+(a_(3)-a_(1))^(2)=0`
`implies a_(1)-a_(2)=0" and "a_(2)-a_(3)=0" and a_(3)-a_(1)=0`
`implies a_(1)=a_(2)=a_(3),AA a_(1),a_(2),a_(3) inR`
So, Statement 2 istrue.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|24 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Matching Type Questions|1 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

Let a_(1),a_(2),a_(3) be terms of an Ap. If (a_(1)+a_(2)+----+a_(p))/(a_(1)+a_(2)----a_(q))=(p^(2))/(q^(2)), p ne q, "then" (a_(6))/(a_(21)) is

If a_(1),a_(2),a_(3)"....." are in GP with first term a and common ratio r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

If (1 + x+ 2x^(2))^(20) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(40) x^(40) . The value of a_(0) + a_(2) + a_(4) + …+ a_(38) is

Differentiate |x|+a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)

The value of lim_(ntooo)a_(n) when a_(n+1)=sqrt(2+a_(n)), n=1,2,3, ….. is

If (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

In a four-dimensional space where unit vectors along the axes are hati,hatj,hatk and hatl, and a_(1),a_(2),a_(3),a_(4) are four non-zero vectors such that no vector can be expressed as a linear combination of other (lamda-1) (a_(1)-a_(2))+mu(a_(2)+a_(3))+gamma(a_(3)+a_(4)-2a_(2))+a_(3)+deltaa_(4)=0 , then

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(0),a_(1) " and " a_(2) are in A.P , the value of n is

Let (a_(1),b_(1)) and (a_(2),b_(2)) are the pair of real numbers such that 10,a,b,ab constitute an arithmetic progression. Then, the value of ((2a_(1)a_(2)+b_(1)b_(2))/(10)) is