If function \((x + 296 \times 298)\) is a perfect square, then the value of \(x\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
296 and 298 lie one on each side of 297, so their product fits the identity \((a-b)(a+b)=a^2-b^2\).
Taking \(a=297\) and \(b=1\) in the identity: \(296\times298=(297-1)(297+1)=297^2-1\)
So \(x+296\times298=x+297^2-1\), which falls 1 short of the square \(297^2\) unless \(x\) makes up that 1
With \(x=1\) this is \(297^2\), a perfect square; with 0, 2 or 3 it falls just below or just above \(297^2\) and is not a perfect square