Question

What should be added to 4x²-3x²+1 to make it a perfect square​

Answer 1

$im \: guessing \: its \: 4x {}^{2} - 3x + 1 \\ (correct \: me \: if \: im \: wrong)$

$(a - b) {}^{2} = a {}^{2} - 2ab + {b}^{2}$

$4x {}^{2} = a {}^{2} \: \: \: \: \: \: \: \: \: \: \: b {}^{2} = 1 \\ a = 2x \: \: \: \: \: \: \: \: \: \: \: \: \: \: b = 1$

$(2x - 1) {}^{2} = 4x {}^{2} -4x + 1$

$we \: need \: to \: add \: a \: - x \\ \: to \: the \: original \: equation$

Note that this problem can be approached in many ways. For instance, we can add to the b² term instead of changing the middle term...

Answer 2

You could solve this by using completing the square and simplifying