Question

The number of real roots of the equation `tan^-1sqrt(x(x + 1)) + sin^-1sqrt(x^2 + x + 1) = π/4` is ______.

Options

• 0

• 4

• 1

• 2

Answer 1

The number of real roots of the equation `tan^-1sqrt(x(x + 1)) + sin^-1sqrt(x^2 + x + 1) = π/4` is 0.

Explanation:

Given, `tan^-1sqrt(x(x + 1)) + sin^-1sqrt(x^2 + x + 1) = π/4`

As x² + x ≥ 0

⇒ x² + x + 1 ≥ 1

But x² + x + 1 ≤ 1 as sin^–1x ⇒ x∈[–1, 1]

So, x² + x = 0

⇒ x = 0, –1

Put x = 0, –1 does not satisfies the original equation

⇒ No solution