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
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
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.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
