Home
Class 12
MATHS
If a, b, c, d are distinct integers in A...

If a, b, c, d are distinct integers in A. P. Such that `d=a^2+b^2+c^2`, then a + b + c + d is

Text Solution

Verified by Experts

The correct Answer is:
2
`a+3k=a^(2)+(a+k)^(2)+(a+2k)^(2)` (1)
(where k is the common difference of A.P)
`rArr5k^(2)+3(2a-1)k+3a^2)-a=0` (2)
`rArr9(2a-1)^(2)-20(3a^(2)-a)ge0(becausek is "real")`
`rArr24a^(2)+16a-9le0`
`rArr-1/3-(sqrt(70))/12ltalt-1/3+(sqrt(70))/12`
`rArrk=0`,3/5 [Not possible]
When a=-1
`5k^(2)-9k+4=0`
`rArrk=1,4/5rArrk=1` (since k is an integer)
`thereforea=-1,b=0,c=1,d=2`
`rArra+b+c+d=2`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.3|9 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.4|13 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.1|3 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

If a,b,c,d are distinct integers in A.Puch that d=a^(2)+b^(2)+c^(2), then a+b+c+d is

If a,b,c,d are distinct integers in an A.P. such that d=a^(2)+b^(2)+c^(2), then find the value of a+b+c+d

If a,b,c,d are four distinct positive numbers in G.P.then show that a+d>b+c.

Let a, b, c, d be distinct integers such that the equation (x - a) (x -b) (x -c)(x-d) - 9 = 0 has an integer root 'r', then the value of a +b+c+d - 4r is equal to :

if a,b,c and d are distinct integers such that a+b+c+d=17, then the real roots of (x-a)(x-b)(x-c)(x-d)=4 are

if a,b, c, d and p are distinct real number such that (a^(2) + b^(2) + c^(2))p^(2) - 2p (ab + bc + cd) + (b^(2) + c^(2) + d^(2)) lt 0 then a, b, c, d are in