Progression (Sequence and Series)Hard
Question
With usual notations in ᐃABC, it is given that r1, r2, r3 are in harmonic progression. The perimeter of triangle is 24 units and area is 24 square units, then -
Options
A.a & c are roots of equation x2 - 16x + 63 = 0
B.a & c are roots of equation x2 - 16x + 60 = 0
C.r2 + r = 8
D.r2 + r = 10
Solution
r1, r2, r3 in H.P. ⇒ a, b, c are in A.P.
2s = a + b + c = 24 ⇒ b = 8
⇒ a + c = 16, s = 12
ᐃ =
⇒ ac = 60
⇒ x2 - 16x + 60 = 0 has roots a & c
r2 + r = r1, r2, r3 in H.P. ⇒ a, b, c are in A.P.
2s = a + b + c = 24 ⇒ b = 8
⇒ a + c = 16, s = 12
ᐃ = ⇒ ac = 60
⇒ x2 - 16x + 60 = 0 has roots a & c
r2 + r =
2s = a + b + c = 24 ⇒ b = 8
⇒ a + c = 16, s = 12
ᐃ =
⇒ ac = 60⇒ x2 - 16x + 60 = 0 has roots a & c
r2 + r = r1, r2, r3 in H.P. ⇒ a, b, c are in A.P.
2s = a + b + c = 24 ⇒ b = 8
⇒ a + c = 16, s = 12
ᐃ =
⇒ ac = 60⇒ x2 - 16x + 60 = 0 has roots a & c
r2 + r =
Create a free account to view solution
View Solution FreeMore Progression (Sequence and Series) Questions
Geometric mean of 3, 9 and 27 is-...If (m + 2)th term of an A.P. is ( m+2)2 − m2, then its common difference is-...The sum of the first ten terms of the geometric progression is S1 and the sum of the next ten terms (11th through 20th) ...A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring ...If sum of 3 terms of a G.P. is S. product is P, and sum of reciprocal of its terms is R, then P2 R3 equals to -...