If a^{x-2}(a² x+2}+a¹-x})=a^{-3}(a^{9}+a²) , then the value of x is;

Correct Answer is : a negative integer.

Correct Answer is : a negative integer.

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Question : 10 of 86

Marks: +1, -0

a^{x-2}(a^{2 x+2}+a^{1-x})=a^{-3}(a^{9}+a^{2})

x

is;

Solution:

Concept:

Simplify the equation using laws of indices, then equate exponents.

Explanation:

Left side:

a^{x-2}(a^{2x+2}+a^{1-x})

expands to

a^{(x-2)+(2x+2)} + a^{(x-2)+(1-x)} = a^{3x} + a^{-1}

Right side:

a^{-3}(a^9+a^2) = a^{-3+9} + a^{-3+2} = a^6 + a^{-1}

Thus

a^{3x} + a^{-1} = a^6 + a^{-1}

. Cancel

a^{-1}

to get

a^{3x} = a^6

Since

a>0

and

a\neq1

, equate exponents:

3x=6 \Rightarrow x=2

x=2

is a positive integer.

Answer:

The value of

x

2

, which is a positive integer. Option C.

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