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Question 9

If $$\sqrt{\frac{19^8 + 19^x}{19^x + 1}} = 361$$, then $$x$$ satisfies the equation

Solution

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Squaring the equation on both sides we get

 $$19^8 + 19^x = 19^4(19^x + 1)$$

$$19^8 - 19^4 = 19^x(19^4 - 1)$$,

$$19^4(19^4 - 1) = 19^x(19^4 - 1)$$ 

Hence $$ x = 4$$. 

Substituting $$x = 4$$ in the options, only  option 4 satisfies the condition

$$3(16) - 11(4) - 4 = 48 - 48 = 0$$ 

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