Question : The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.
Option 1: 630
Option 2: 540
Option 3: 450
Option 4: 360

Question

Question : The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.

Option 1: 630

Option 2: 540

Option 3: 450

Option 4: 360

Team Careers360 · Accepted Answer

Correct Answer: 540

Solution : Let $a$ and $b$ be the two numbers.
So, $ab$ = 144 and $(a-b)^2 = 324$
⇒ $ab$ = 144 and $(a-b) = 18 $
We know that $(a+b)^2 = (a-b)^2 + 4ab$
⇒ $(a+b)^2 = 324 + 576$
⇒ $(a+b)^2 = 900$
⇒ $(a+b) = 30$
Now, $a^2-b^2$ = $(a-b)×(a-b)$
⇒ $a^2-b^2 = 18 × 30$
$ herefore a^2-b^2 = 540$
Hence, the correct answer is 540.

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Question : The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.Option 1: 630Option 2: 540Option 3: 450Option 4: 360

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Question : The square of the difference between two given natural numbers is 324, while the product of these two given numbers is 144. Find the positive difference between the squares of these two given numbers.
Option 1: 630
Option 2: 540
Option 3: 450
Option 4: 360