If a,b,c are in ap and a+b/2= x,b+c/2=y than the value of (x+y) is (a)2a(b)2b(c)2(a+b)(d)2(b+c)
Answers
Answer:
We have 2b=a+c and b
2
=
a
2
+c
2
2a
2
c
2
.....(i)
On eliminating b, we get
8a
2
c
2
=(a
2
+c
2
+2ac)(a
2
+c
2
)
Which can be arranged as
(a
2
+c
2
−2ac)(a
2
+c
2
+4ac)=0
⇒either a=c or (a+c)
2
+2ac=0
If a=c then a=b=c
⇒ a, b, c may be treated as three numbers in G .P.
If (a+c)
2
+2ac=0, then by using (i) choice (D) follows.
Answer:x + y = a + 2b + c ÷ 2Step-by-step explanation:
a + b ÷ 2 = x
b + c ÷ 2 = y
a + b = 2x 1
+ b = 2x1b + c = 2y 2
+ b = 2x 1b + c = 2y21 + 2
+ b = 2x1b + c = 2y 21 + 22x + 2y = a + b + b + c
+ b = 2x 1b + c = 2y 21 + 22x + 2y = a + b + b + c2x + 2y = a + 2b + c
+ b = 2x 1b + c = 2y21 + 22x + 2y = a + b + b + c2x + 2y = a + 2b + c2 ( x + y ) = a + 2b + c
+ b = 2x 1b + c = 2y 21 + 22x + 2y = a + b + b + c2x + 2y = a + 2b + c2 ( x + y ) = a + 2b + cx + y = a + 2b + c ÷ 2