Let the sum of three real roots of the equation 2333x – 2 + 2111x + 2 = 2222x + 1 + 1 be m/n, where m and n are relatively prime positive integer. Find m + n.
Let the sum of three real roots of the equation 2333x – 2 + 2111x + 2 = 2222x + 1 + 1 be m/n, where m and n are relatively prime positive integer. Find m + n.
Option 1 -
113
Option 2 -
313
Option 3 -
311
Option 4 -
213
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:Let y = 2111x then,
y3 – 8y2 +16y – 4 = 0
Let three real roots be a, b and c then abc = and corresponding values of x be x1, x2, and x3\
111 (x1 + x2 + x3) = 2
x1 + x2 + x3 = 2/111
m + n = 2 + 111 = 113
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