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in Sets, relations and functions by (50.2k points)

If M is the  number of real solution of cos-1x + cos-1(2x) + π = 0 and N is the number of values of x satisfying the equation sin-1(5/x) + sin-1(12/x) = π/2, then find the value of M + N + 4

1 Answer

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Best answer

Given equation is

cos-1x + cos-1(2x) + π = 0

⇒ 9x2 = 0

⇒ x = 0

But x = 0 does not satisfy the equation.

So it has no solution.

Therefore M = 0

Clearly, x = 13 only satisfies the equation. Thus, N = 1.

Hence, the value of M + N + 4 = 5.

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