Question

sin x + cos x = y² – y +a has no value of x for any y if ‘a’ belongs to

• A. (0, $\sqrt{3}$)
• B. (–$\sqrt{3}$, 0)
• C. (–∞ , –$\sqrt{3}$)
• D. ($\sqrt{3}$, ∞)

Answer 1

Answer: (D)

($\sqrt{3}$, ∞)

Answer 2

y² – y + a = $\left( y - \frac{1}{2} \right)^{2} + a - \frac{1}{4}$ . Since –$\sqrt{2}$ ≤ sin x + cos

x ≤$\sqrt{2}$, given equation will have no real value of x for any

y if $a - \frac{1}{4}$>$\sqrt{2}$

i.e. a ∈ $\left( \sqrt{2} + \frac{1}{4},\infty \right)$

⇒ a ∈ ($\sqrt{3}$, ∞) ( as $\sqrt{2}$+ 1/4 < $\sqrt{3}$ )