The number of the real roots of the equation...
The number of the real roots of the equation 2 cos(x(x + 1)) = 2x + 2-x is
• a)
2
• b)
1
• c)
infinite
• d)
0
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The number of the real roots of the equation 2 cos(x(x + 1)) = 2x + 2...
2 cos(x(x + 1)) = 2x + 2-xThe maximum value of LHS is 2 when cos(x(x + 1)) is 1 and the minimum value of RHS is 2 using AM ≥ GM
Hence LHS and RHS can only be equal when both sides are 2.
For LHS, cosx(x+1) =1 => x(x+1) =0 => x=0,-1
For RHS minimum value, x=0
Hence only one solution x=0
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The number of the real roots of the equation 2 cos(x(x + 1)) = 2x + 2-x isa) 2b) 1c) infinited) 0Correct answer is option 'B'. Can you explain this answer?
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