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What number must be added to the expression 16a² - 12a to make a perfect square ?

1 $\frac{9}{4}$ $\frac{9}{4}$
2 $\frac{11}{2}$ $\frac{{11}}{2}$
3 $\frac{13}{2}$ $\frac{{13}}{2}$
416

Answer:- 1

Explanation:-

Solution:

\begin{aligned} {(a - b)}^{2} = a^{2} + b^{2} + 2 a b \\ 16 a^{2} - 12 a \\ = (4 a)^{2} - 2 \times 4 a \times \frac{3}{2} + {(\frac{3}{2})}^{2} \\ Number be added \\ = {(\frac{3}{2})}^{2} \\ = \frac{9}{4} \end{aligned}

$\eqalign{ & {\left( {a - b} \right)^2} = {a^2} + {b^2} + 2ab \cr & 16{a^2} - {\text{12}}a \cr & = {(4a)^2} - 2 \times 4a \times \frac{3}{2} + {\left( {\frac{3}{2}} \right)^2} \cr & {\text{Number be added}} \cr & {\text{ = }}{\left( {\frac{3}{2}} \right)^2} \cr & = \frac{9}{4} \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} {(a - b)}^{2} = a^{2} + b^{2} + 2 a b \\ 16 a^{2} - 12 a \\ = (4 a)^{2} - 2 \times 4 a \times \frac{3}{2} + {(\frac{3}{2})}^{2} \\ Number be added \\ = {(\frac{3}{2})}^{2} \\ = \frac{9}{4} \end{aligned}

$\eqalign{ & {\left( {a - b} \right)^2} = {a^2} + {b^2} + 2ab \cr & 16{a^2} - {\text{12}}a \cr & = {(4a)^2} - 2 \times 4a \times \frac{3}{2} + {\left( {\frac{3}{2}} \right)^2} \cr & {\text{Number be added}} \cr & {\text{ = }}{\left( {\frac{3}{2}} \right)^2} \cr & = \frac{9}{4} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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