Solve the following mathematical problems:

Two numbers x, y are in G.P and their sum is 30. Also, the sum of their squares is 468. Find the numbers.

Created: 5 months ago | Updated: 2 weeks ago
Job Solution Rupali Bank Ltd Rupali Bank Ltd. || Officer (22-11-2019) || 2019 গণিত
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Let, one number is x and another one is y

According to question

x + y = 30 .......... (i)

And x2 + y2 = 468 ............(ii)

From equation (i), x + y = 30

⇒x=30-y........ (iii)

putting x = 30 - y in equation (ii)

x2 + y2 = 468

=(30 - y)2 + y2 = 468

= 900 - 60y + y2 + y2 = 468

=2y2 - 60y + 432 = 0

=y2 - 30y + 216 = 0

=y2 - 18y - 12y + 216 = 0

=y(y - 18) - 12(y - 18) = 0

=(y - 18)(y - 12) = 0

Here, y - 18 = 0

∴y = 18

Or, y - 12 = 0

∴ y = 12

Putting y = 18 in equation (iii), we get

x = 30 - 18 = 12

∴x = 12

Putting y = 12 , in equation (iii) we get

x = 30 - 12 = 18

∴x = 18

(answer) (x, y) = (12, 18) Or, (18, 12).

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