Question

what must be added to 4x^2+12x+5 to make it as a perfect square​

Answer 1

$Let \: P \: should \:be \: added \:to \\4x^{2} + 12x + 5 \: to \: make \: it \: a \: perfect \:square$

$Let \: 4x^{2} + 12x + 5 + p = a^{2} + 2ab + b^{2}$

$\implies (2x)^{2} + 2\times 2x \times 3 + ( 5 + p ) \\= {2} + 2ab + b^{2}$

/* Compare middle term and third terms of bothsides, we get*/

$Here,2\times 2x \times 3 = 2ab$

$a = 2x ,\: b = 3$

$5 + p = b^{2}\: (third \:term)$

$\implies 5 + p = 3^{2}$

$\implies p = 9 - 5$

$\implies p = 4$

Therefore.,

$\pink { 4 \: should \:be \: added \:to }$

$\pink {4x^{2} + 12x + 5 \: to \: make \: it \: a }$

$\pink { perfect \:square}$

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