Question 9
If $$\sqrt{\frac{19^8 + 19^x}{19^x + 1}} = 361$$, then $$x$$ satisfies the equation
Solution
Squaring gives $$19^8 + 19^x = 19^4(19^x + 1)$$, so $$19^8 - 19^4 = 19^x(19^4 - 1)$$, that is $$19^4(19^4 - 1) = 19^x(19^4 - 1)$$ and hence $$x = 4$$. Substituting $$x = 4$$ in the options, only $$3(16) - 11(4) - 4 = 48 - 48 = 0$$ holds.
Get AI Help
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Session:Free CAT Mentorship
Phone:
Date:
Time:
Enter OTP
Didn't receive the OTP?
