Question

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)​

Answer 1

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 2

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