Mes. monthly
(Chp.3)
(40) The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find
the two numbers.
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The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Let the larger number be x

And, the square of the smaller number be 8x

x² − 8x = 180

⇒ x² − 8x − 180 = 0

⇒ x² − (18 − 10)x − 180 = 0

⇒ x² − 18x + 10x − 180 = 0

⇒ x (x − 18) + 10(x − 18) = 0

⇒ (x − 18) (x + 10) = 0

⇒ x − 18 = 0, x + 10 = 0

⇒ x = 18, x = −10

⇒ x = −10, 18

Either, x = −10 and x = 18

x = 18 (Positive value)

Now, the square of the smaller number = 8x = 8 × 18 = 144

So, the square of the smaller number = = 12

water and alcohols have similar properties because water molecules contain hydroxyl groups that can form hydrogen bonds with other water molecules and with alcohol molecules, and likewise alcohol molecules can form hydrogen bonds with other alcohol molecules as well as with water.