Question

quantities x,8,y(x not equal to y) are in GP and x, y, - 8 are in AP find the value of x and y.​

Answer 1

Here is ur answer...

given:-

a = x , b = 8 , c = y

when numbers are in gp , then

b^2 = ac

8^2 = xy

64 = xy

y = 64 / x ----- 1

given:-

a = x , b= y , c = -8

when numbers are in ap then

2b = a + c

2y = x - 8. ---- 2

from eq. 1 put the value of y in eq.2

(2×64 )/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

x - 16 = 0 x + 8 = 0

x = 16 x = -8

when x = 16

put this value in eq. 1

y = 64 / x

y = 64 / 16

y = 4

when x = -8

put this value again eq.1

y = 64 / -8

y = -8

Answer:-

x = 16 y = 4

x = -8 y = -8

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