The equation {3} x+ x=4 has

Correct Answer is : No solution

Correct Answer is : No solution

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CGPET 2019 Solved Paper

Section: Mathematics

Question : 137 of 150

Marks: +1, -0

The equation

\sqrt{3} \sin x+\cos x=4

has

Solution:

Given equation is,

\sqrt{3} \sin x+\cos x=4

Let

\sin x=t

\because \cos x=\sqrt{1-\sin^{2} x} \qquad \therefore \cos x=\sqrt{1-t^{2}}

Now,

\sqrt{3} t+\sqrt{1-t^{2}}=4, \sqrt{1-t^{2}}=4-\sqrt{3} t

Squaring both sides, we get

1-t^{2} =16+3t^{2}-8 \sqrt{3} t

\Rightarrow 4 t^{2}-8 \sqrt{3} t+15 =0

Discriminant

(D) =(8 \sqrt{3})^{2}-4(4)(15)

=192-240=-48 < 0

So, the equation has imaginary roots, So, there are no solutions.

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