Question

Solve for x
√3x2+x+5= x-3​

Answer 1

Step-by-step explanation:

Now, 3x

2

+x+5⩾0

This is because b

2

−4ac=1−4×5×3

=−59 (roots are imaginary)

3x

2

+x+5=(x−3)

2

=x

2

+9−6x and x−3⩾0

2x

2

+7x−4=0

2x

2

+8x−x−4=0

2x(x+4)−1(x+4)=0

(2x−1)(x+4)=0

x=

2

1

and−4 but x≥3

∴ No solution.

Answer 2

Answer:

$\sqrt{3} {x}^{2} + x + 5 = x - 3 \\ \\ \\ = > \sqrt{3} {x}^{2} + 5 + 3 = x - x \\ \\ = > \sqrt{3} {x}^{2} + 8 = 0 \\ \\ = > \sqrt{3} {x}^{2} = - 8 \\ \\ \\ = > {x}^{2} = \frac{ - 8}{ \sqrt{3} } \\ \\ \\ = > x = - \sqrt{(\frac{ 8}{ \sqrt{3} } ) } \\ \\ \\ \\ = >x = -\frac{2 \sqrt{2} }{3}$

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