JAMIA 2022 — Mathematics PYQ

Step 1: Assume the Numbers

Let the three numbers be:

where $a$ is the middle term and $d$ is the common difference.

Step 2: Use the Sum Condition

The problem states that the sum of these three numbers is $-3$:

Combining the terms, the $d$ cancels out:

Step 3: Use the Product Condition

The problem states that the product of these three numbers is $8$:

Substitute $a=-1$ into the equation:

Using the difference of squares identity $(x-y)(x+y)=x^2-y^2$:

Step 4: Identify the Numbers

Using $a=-1$ and $d=3$ (or $d=-3$, the set remains the same):

• First number: $a-d=-1-3=-4$

• Second number: $a=-1$

• Third number: $a+d=-1+3=2$

The three numbers are $-4,-1,\text{ and }2$.

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Step 5: Find the Sum of Squares

The question asks for the sum of the squares of these numbers:

Final Answer

The sum of the squares of the numbers is 21.