Question

Sum of squares of two numbers is 3341 and difference is 891. Find numbers.

• A. 35 and 46
• B. 35 and 50
• C. 40 and 55
• D. 45 and 60

Hint:

When both sum and difference of squares are given, add the equations first to eliminate one variable quickly.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The sum of the squares of two numbers is 3341 and the difference of their squares is 891. We need to find the two numbers.

Step 2: Key Formula or Approach:
Let the numbers be \(x\) and \(y\). Given: \[ x^2+y^2=3341 \] \[ x^2-y^2=891 \] Using addition of equations: \[ (x^2+y^2)+(x^2-y^2)=3341+891 \]

Step 3: Detailed Explanation:
Add the two equations: \[ 2x^2=4232 \] \[ x^2=2116 \] \[ x=\sqrt{2116}=46 \] Now substitute into: \[ x^2+y^2=3341 \] \[ 2116+y^2=3341 \] \[ y^2=3341-2116 \] \[ y^2=1225 \] \[ y=\sqrt{1225}=35 \] Therefore, the two numbers are: \[ 35 \text{ and } 46 \]

Step 4: Final Answer:
Hence, the correct option is: \[ \boxed{\text{(A) 35 and 46}} \]