Question

31. If the positive numbers 3, x, 5, y are in a G. P. then : (x, y)=
a)(3 √15,2√5 ) b) (3√5, 15√5) c) (2√15, 3√5) d) none
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Answer 1

Answer:

Option D : None of the Above

Step-by-step explanation:

For a series to be in GP, the following condition must be satisfied.

Condition 1: The common ratio must be same.

⇒ a₂ / a₁ = a₃ / a₂ = a₄ / a₃

Applying the condition here, we get,

⇒ x / 3 = 5 / x = y / 5

Taking first two cases, we get,

⇒ x / 3 = 5 / x

Cross Multiplying we get,

⇒ x² = 5 × 3 = 15

⇒ x = √15

Now taking second case, we get,

⇒ 5 / x = y / 5

Cross Multiplying we get,

⇒ 25 = xy

⇒ 25 = √15 × y

⇒ 25 / √15 = y

⇒ 5√5 / 3 = y

Hence ( x,y ) = ( √15, 5√5/3 )

Hence Option D is the right answer.