Which of the following equations has/have no real root(s)?

2 cos (\frac{x}{3}) = 2^{x} + 2^{- x}

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2^{| x |} = sin x^{2}

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3 | sin \sqrt{x} | = | cos x |

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None of these

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Solution

The correct option is B $2^{| x |} = sin x^{2}$
From the given options only $O p t : [B]$ have no real roots

we know that $sin θ$ lies in $[- 1, 1]$

$\Rightarrow - 1 \leq sin x^{2} \leq 1$

but $2^{| x |} > 1$ so for $2^{| x |} = sin x^{2}$ has no real roots

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Which of the following equations has/have no real root(s)?

The correct option is B 2|x|=sinx2From the given options only Opt:[B] have no real roots we know that sinθ lies in [−1,1]⇒−1≤sinx2≤1 but 2|x|>1 so for 2|x|=sinx2 has no real roots

The correct option is B $2^{| x |} = sin x^{2}$
From the given options only $O p t : [B]$ have no real roots

we know that $sin θ$ lies in $[- 1, 1]$

$\Rightarrow - 1 \leq sin x^{2} \leq 1$

but $2^{| x |} > 1$ so for $2^{| x |} = sin x^{2}$ has no real roots