Question

which of the following should be added to make x ^ 4 + 64 a perfect square?

a) 4x^2
b)16x^2
c)8x^2
d)-8x^2

step by step answer needed

Answer 1

Answer:

option b) 16x^2 is that

Answer 2

$Let \: p \: should \: be \: added \: to \\to \:make \: x^{4} + 64 \: perfect \:square .$

$x^{4} + 64 + p = ( m + n )^{2}$

$\implies (x^{2})^{2} + 8^{2} + p = m^{2}+n^{2} + 2mn$

/* Compare bothsides of the equation, we get */

$m = x^{2} , n = 8 \\p = 2mn$

$\implies p = 2 \times x^{2} \times 8 \\= 16x^{2}$

Therefore.,

$\green {16x^{2}}\red{ \: should \: be\: added \:to\:make}$

$\red{ x^{4} + 64 \: perfect \:square .}$

$Option \: \pink { (b) } \: is \: correct$

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