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The numbers x, 8, y are in G.P. and the numbers x, y, –8 are in A.P. The value of x and y are
- a)(–8, –8)
- b)(16, 4)
- c)(8, 8)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The numbers x, 8, y are in G.P. and the numbers x, y, –8 are in ...
So for a GP a,b,c we have b = √ac
and a AP A,B,C We have 2B = A + C
so here
x,8,y is in GP so 8 = √xy ⇒ 64/x = y . .... i
and x,y,-8 in AP so 2y = x - 8 .... ii
using i and ii
we get
128/x = x - 8
⇒ 128 = x^2 - 8x
⇒ x^2 - 8x - 128 = 0
⇒ x^2 - 16x + 8x - 128 = 0
⇒ x(x - 16) + 8(x - 16) = 0
⇒(x - 16)(x + 8) = 0
so x = 16 or - 8
so y = 4 or -8
so the GP is 16,8,4 but -8,8,-8 is not possible
and for the AP
16,8,-8 again -8,-8,-8 is not possible
so values fo x = 16 and y = 4
Most Upvoted Answer
The numbers x, 8, y are in G.P. and the numbers x, y, –8 are in ...
Given: x, 8, y are in G.P. and x, y, 8 are in A.P.
To find: Value of x and y
Solution:
Let the common ratio of the G.P. be r.
Then, according to the given information, we have:
y = 8r
and
x/y = r
=> x = ry
Also, x, y, 8 are in A.P.
So, we have:
y - x = x - 8
=> y - ry = ry - 8
=> y(1 - r) = 8(1 - r)
=> y = 8
=> x = ry = r(8) = 8r = 4
Therefore, the value of x and y is (4, 8).
Hence, option B is the correct answer.
To find: Value of x and y
Solution:
Let the common ratio of the G.P. be r.
Then, according to the given information, we have:
y = 8r
and
x/y = r
=> x = ry
Also, x, y, 8 are in A.P.
So, we have:
y - x = x - 8
=> y - ry = ry - 8
=> y(1 - r) = 8(1 - r)
=> y = 8
=> x = ry = r(8) = 8r = 4
Therefore, the value of x and y is (4, 8).
Hence, option B is the correct answer.
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The numbers x, 8, y are in G.P. and the numbers x, y, –8 are in ...
Ans is b I think option a in ap d is 0 ap difference doesn't come in 0 and c option also same that so option is c
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