Question

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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Answer 1

Question:-

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.

Solution:-

Let the larger number be x

And, the square of the smaller number be 8x

ATQ ,

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

$\therefore$ 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 = $\sqrt{144}$ = 12

The two numbers are 18 and 12. [Answer]