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Question

Solve 5x+1+52x=53+1 [4 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark
Answer: 2 Marks


We have,

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.

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