Question

Qᴜᴇꜱᴛɪᴏɴ:-


The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

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Answer 1

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Answer:

L.H.S. = x2 – y2

= (p sec θ + q tan θ)2 – (p tan θ + q sec θ)2

= p2 sec θ + q2 tan2 θ + 2 pq sec 2 tan 2 -(p2 tan2 θ + q2 sec2 θ + 2pq sec θ tan θ)

= p2 sec θ + 2 tan2 θ + 2pq sec θ tan θ – p2 tan2 θ – q2 sec θ – 2pq sec θ tan θ

= p2(sec2 θ – tan2 θ) – q2(sec?2 θ – tan2 θ) =

= p2 – q2 …[sec2 θ – tan2 θ = 1

= R.H.S.

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Answer 2

Step-by-step explanation:

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Let the two consecutive natural numbers which are multiples of 3 be 3x and 3(x + 1).

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Now, 3x(3x + 3) = 810 ⇒ x2 + x = 90 ⇒ x2 + x – 90 = 0 ⇒ (x + 10) (x – 9) = 0 ⇒ x = 9 or x = – 10

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Rejecting negative value of x, because numbers are natural.

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We have x = 9.

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Hence, the required numbers are 27 and 30.