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03 Dec 2020, 01:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (01:57) correct
41%
(02:07)
wrong
based on 280
sessions
History
Date
Time
Result
Not Attempted Yet
What is the sum of all solutions of \(49^x + 7^{(1-2x)} = 8\) ?
A. -1
B. -1/2
C. 0
D. 1/2
E. 1
Are You Up For the Challenge: 700 Level Questions
A. -1
B. -1/2
C. 0
D. 1/2
E. 1
Are You Up For the Challenge: 700 Level Questions
03 Dec 2020, 03:32
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49^x + 7^(1-2x) = 8
or, 7^(2x) + 7^(1-2x) = 8
or, 7^(2x) + 7/7^(2x) = 8
or, a+7/a =8 [ let, 7^(2x) =a ]
or, a^2-8a+7=0
or, a=1, 7
so, 7^(2x) =1 =7^0
or,x=0
and, 7^(2x)=7 = 7^1
or, x=1/2
therefore, the sum of all solutions of 49^x + 7^(1-2x) = 8 is (0+1/2) =1/2
correct answer is D
or, 7^(2x) + 7^(1-2x) = 8
or, 7^(2x) + 7/7^(2x) = 8
or, a+7/a =8 [ let, 7^(2x) =a ]
or, a^2-8a+7=0
or, a=1, 7
so, 7^(2x) =1 =7^0
or,x=0
and, 7^(2x)=7 = 7^1
or, x=1/2
therefore, the sum of all solutions of 49^x + 7^(1-2x) = 8 is (0+1/2) =1/2
correct answer is D
03 Dec 2020, 05:27
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IMO D
Take 49^x = y
=> quadratic equation in terms of y. This has roots: 7 and 1.
=> 49^x = 1 OR 49^x = 7
=> x=0 OR x=1/2
Sum of roots= 0 + 1/2 = 1/2
Take 49^x = y
=> quadratic equation in terms of y. This has roots: 7 and 1.
=> 49^x = 1 OR 49^x = 7
=> x=0 OR x=1/2
Sum of roots= 0 + 1/2 = 1/2
Bunuel
