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SNAP 2014 Question-15

Q.)What should be added to the expression { 16a }^{ 2 }-12a to make it a perfect square?
(a) 9/4
(b) 11/2
(c) 13/2
(d) 16

Solution : { 16a }^{ 2 }-12a = { 16(a }^{ 2 }-\frac { 12a }{ 16 } )=16({ a }^{ 2 }-\frac { 3 }{ 4 } a)

To make it a perfect square , we can do it like this

16{ \{ a }^{ 2 }-2X\frac { 3 }{ 8 } a+{ (\frac { 3 }{ 8 } ) }^{ 2 }\}

= 16{ \{ a }^{ 2 }-2X\frac { 3 }{ 8 } a+{ (\frac { 3 }{ 8 } ) }^{ 2 }\}

={ \{ 4{ (a }-\frac { 3 }{ 8 } )\}  }^{ 2 }

Hence , the amount which should be added to make ita perfect square = 9/4

Option(a)


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