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 numbers, then a,b,c are in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
c
Since , ` 4a^(2) + 9b^(2) + 16c^(2) = 2(3ab + 6bc+4ca)`
`rArr 8a^(2) + 18b^(2) + 32c^(2) - 12ab - 24bc - 16ca = 0 `
`rArr (4a^(2)- 12ab + 9b^(2)-24bc +16c^(2))`
` + (16c^(2) - 16ca+4a^(2))^(2)=0`
` rArr ` 2a = 3b , 3b = 4c, 4c = 2a
` rArr` 2a = 3b = 4c = k [say]
` rArr a= k/2 , b = k/3, c = k/4 `
` rArr ` are in HP.
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|1 Videos

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 3|1 Videos

  • PROBABILITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|4 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|30 Videos

Similar Questions

Explore conceptually related problems

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 .

If (a^(2)+b^(2)+c^(2))(b^(2)+c^(2)+d^(2))<=(ab+bc+cd)^(2) where a,b,c,d are non-zero real numbers,then they are in

If a^(2)+b^(2)+c^(2)=ab+bc+ca where a,b,c are the sides of a triangle,then the largest angle of that triangle is

If a^(2)+b^(2)+c^(2)=24 and ab+bc+ca=-4, then find a+b+c

If (1)/(a)+(1)/(b)+(1)/(c)=0, where a,b and c are non-zero real numbers,then (a^(2)+b^(2)+c^(2)-ab-bc-ca)/((a+b+c)^(2)) is equal to

If a^(2)+b^(2)+c^(2)=20 and a+b+c=9 , find ab+bc+ca .

If a+b+c=6, a^(2) +b^(2)+ c^(2)=16 , find ab+bc +ca = ?