Quantitative Aptitude – Algebra – Functions – The number of the real roots
Slot -1 – Quantitative Aptitude – Algebra – Functions – The number of the real roots of the equation
The number of the real roots of the equation – Video
Q. The number of the real roots of the equation 2cos (x ( x + 1 ) ) = 2^x + 2^-x is?
1
0
2
infinite
Answer: 1
Solution:
As we know maximum value of cos A = 1 at A =0
So maximum value of 2cos (x ( x + 1 ) ) = 2*1 =2
Minimum value of 2^x + 2^(-x) = 2 ( as the minimum value of k + 1/k = 2 at k = 1) at x = 0
Thus there is only one possible case when 2cos (x ( x + 1 ) ) = 2^x + 2^-x at x =0
So no of real solution =1