Question

Select whether the equation has a solution or not.

Answer 1

Answer: The equation has a solution .

Step-by-step explanation:

Since we have given that

$\sqrt{x+1}=7-2\sqrt{x}$

Squaring on both the sides, we get that,

$x+1=(7-2\sqrt{x})^2\\\\x+1=49+4x-28\sqrt{x}\\\\3x+48-28\sqrt{x}=0$

Let $\sqrt{x}=y\implies x=y^2$

So, our equation becomes,

$3y^2-28y+48=0\\\\y=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\\sqrt{x}=\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3}\\\\x=(\dfrac{14}{3}\pm \dfrac{2\sqrt{13}}{3})^2$

So, $x=\dfrac{248}{9}\pm \dfrac{56\sqrt{13}}{9}$

Hence, the equation has a solution .