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Question : If the sum of squares of two real numbers is 41 and their sum is 9, then the sum of cubes of these two numbers is:

Option 1: 169

Option 2: 209

Option 3: 189

Option 4: 198


Team Careers360 17th Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

Correct Answer: 189


Solution : Let the two numbers be $\text{x}$ and $\text{y}$.
As per the condition of the question,
⇒ $\text{x}^{2} + \text{y}^{2}$ = 41 and  $\text{x + y} = 9$
We know $\text{(x + y)}^{2} = \text{x}^{2} + \text{y}^{2} + \text{2xy}$
Putting values in the given expression:
$\text{(9)}^{2} = 41 + \text{2xy}$
⇒ $\text{2xy} = 81 - 41$
⇒ $\text{xy} = \frac{40}{2} = 20$
Using the formula, $\text{x}^{3} + \text{y}^{3} = \text{(x + y)}^{3}- \text{3xy}\text{(x+y)}$, we get,
$\text{x}^{3} + \text{y}^{3} = \text{(9)}^{3}- 3\times20\times 9$
⇒ $\text{x}^{3} + \text{y}^{3} = 729- 540 = 189$
Hence, the correct answer is 189.

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