Question

If (root 2)^x + (root 3)^x = (root 13)^x/2, then the value of x is

Answer 1

Answer:

Given , (√2)^x + (√3)^x = (√13)^(x/2)

=> (2)^(x/2) + (3)^(x/2) = (√13)^(x/2)

=> [(2)/(√13)]^(x/2) + [(3)/(√13)]^(x/2) = 1

= 13/13

=> [ (2)/(√13) ]^(x/2) + [ (2)/(√13) ]^(x/2)

= (2/√13)² + (3/√13)²

Now, Compare both sides of the equation,

we get:- x/2 = 2 => x = 4.

Hence, the value of “x" is “4".

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Answer 2

$x = 4 \: \: \: \: \: \:$