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The sum of the squares of two numbers is 234 and the square of their difference is 144. Find the product of the two numbers ?
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- 28
- 52
- 36
- 45
Correct Option: D
Let the two numbers be x and y.
Then, x2 + y2 = 234 ...(i)
and (x - y)2 = 144 ...(ii)
Now, (x - y)2 = 144
⇒ x2 + y2 - 2xy = 144
⇒ 234 - 2xy = 144 [using Eq.(i)]
On substituting the value of x2 + y2 from Eq.(i) in Eq.(ii),
we get
2xy = 90
⇒ xy = 45
So, the product of the two numbers is 45.
