CUET UG 2025 — General Test Quantitative Reasoning

The expression $(x + 296 \times 298)$(x+296×298) needs to be a perfect square.

Notice that $296$296 and $298$298 are consecutive even numbers around $297$297:

$$296 = 297 - 1$$296=297−1

$$298 = 297 + 1$$298=297+1

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Using the formula $(a - b)(a + b) = a^2 - b^2$(a−b)(a+b)=a2−b2 with $a = 297$a=297 and $b = 1$b=1:

$$296 \times 298 = (297 - 1)(297 + 1)$$296×298=(297−1)(297+1)

$$= 297^2 - 1^2$$=2972−12

$$= 297^2 - 1$$=2972−1

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Substituting back into the original expression:

$$x + 296 \times 298 = x + (297^2 - 1)$$x+296×298=x+(2972−1)

$$= x + 297^2 - 1$$=x+2972−1

$$= 297^2 + (x - 1)$$=2972+(x−1)

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For this to be a perfect square, the simplest case is when it equals $297^2$2972 exactly.

This occurs when:

$$x - 1 = 0$$x−1=0

$$x = 1$$x=1

Therefore, the value of $x$x is $1$1.