Question

${4}^{x} - 3( {2}^{x + 3} ) + 128 = 0 \\ sum \: of \: the \: roots \: of \: equation$
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Answer 1

Answer:

Given equation

4x−3(2x+3)+128=0

⇒(22)x−3(2x⋅23)+128=0

⇒(2x)2−3(2x⋅8)+128=0

Taking 2x=y

the equation becomes

⇒y2−24y+128=0

⇒y2−16y−8y+128=0

⇒y(y−16)−8(y−16)=0

⇒(y−16)(y−8)=0

So y=8 and y=16

when y=8

⇒2x=23

⇒x=3

when y=16

⇒2x=24

⇒x=4

Hence roots are 3and4

So the sum of the roots is

=3+4

=7