Home
Class 12
MATHS
If a, b, c are real numbers forming an A...

If `a`, `b`, `c` are real numbers forming an `A.P.` and `3+a`, `2+b`, `3+c` are in `G.P.` , then minimum value of `ac` is

A

`-4`

B

`-6`

C

`3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `:. (2+b)^(2)=(3+a)(3+c)` ,brgt `:. 4+b^(2)+4b=9+3(a+c)+ac`
`:.4+b^(2)+4b=9+6b+ac` ,brgt `:.ac=b^(2)-2b-5=(b-1)^(2)-6`
`:.ac ge -6`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Comprehension|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|4 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

If a,b,c are three unequal numbers such that a,b,c are in A.P. and (b-a) ,. (c-b) ,a are in G.P., then the value of a:b: c is-

If a , b , c , are three unequal number such that a , b ,c are in A.P and (b-a),(c-b) , a are in G.P then find a: b: c .

If three positive real number a,b,c are in AP with abc =4 , then the minimum value of b is

If In (a + c), In(c - a) , In(a - 2b + c) are in A.P., then

Suppose a,b,c are in A.P and a^2 , b^2 , c^2 are in G.P if a

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a. a/c+c/a b. a/c-c/a c. b/q + q/b d. b/q - q/b

Suppose a,b, c are in A.P. and a^(2) , b^(2),c^(2) are in G.P. if a lt b lt c and a+b+c =3/2, then the value of a is-

Three unequal numbers a, b, c are in A.P. and a, (b-a), (c-a) are in G.P. Prove that, a : b : c = 1 : 3 : 5 .

Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c and a+b+c=3/2 then the value of a is

If the angles A,B,C of a triangle are in A.P. and sides a,b,c, are in G.P., then prove that a^2, b^2,c^2 are in A.P.