The equation sqrt {3 {x^2} + x + 5} = x | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Consider $\sqrt{3 x^{2}+x+5}=x-3$

Squaring both the sides, we get

$3 x^{2}+x+5=(x-3)^{2}$

$\Rightarrow 3 x^{2}+x+5=x^{2}+9-6 x$

$\Rightarr

Vedclass · Accepted Answer

no solution

Vedclass · Answer

Consider $\sqrt{3 x^{2}+x+5}=x-3$

Squaring both the sides, we get

$3 x^{2}+x+5=(x-3)^{2}$

$\Rightarrow 3 x^{2}+x+5=x^{2}+9-6 x$

$\Rightarrow 2 x^{2}+7 x-4=0$

$\Rightarrow 2 x^{2}+8 x-x-4=0$

$\Rightarrow 2 x(x+4)-1(x+4)=0$

$\Rightarrow x=\frac{1}{2}$ or $x=-4$

For $x=\frac{1}{2}$ and $x=-4$

$L.H.S.$ $
eq$ $R.H.S.$ of equation, $\sqrt{3 x^{2}+x+5}$ $=x-3$

Also, for every $x \in R, \mathrm{LHS} 
eq \mathrm{RHS}$ of the given equation. 

$	herefore $ Given equation has no solution.

The equation $\sqrt {3 {x^2} + x + 5} = x - 3$ , where $x$ is real, has

Similar Questions

If $x$ be real, then the minimum value of ${x^2} - 8x + 17$ is

Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?

If graph of $y = ax^2 -bx + c$ is following, then sign of $a$, $b$, $c$ are

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0,$ is

If the product of roots of the equation ${x^2} - 3kx + 2{e^{2\log k}} - 1 = 0$ is $7$, then its roots will real when