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Question

Solve 5x+1+52x=53+1 



A

x = 2

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B

x = 7

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C

x = -1

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D

x = 6

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Solution

The correct options are
A

x = 2


C

x = -1


5x+1+52x=53+1

5x×5+52×5x=126

5x×5+255x=126......(1)

Let 5x=y

Then (1) reduces to,

5y+25y=126

5y2126y+25=0

5y2125yy+25=0

5y(y25)1(y25)=0

(y25)(5y1)=0

y25=0  or  5y1=0

y=25  or  y=15

5x=25  or  5x=15

5x=52  or  5x=51

x=2  or  x=1

Roots of the equation are 2 and -1.


Mathematics

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