Solve the following equation:

$$
\sqrt{x+6}+\sqrt{x+1}=\sqrt{7 x+4} .
$$
Squaring both sides and rearranging:

$$
2 \sqrt{x^{2}+7 x+6}=5 x-3
$$

squaring again:

$$
4\left(x^{2}+7 x+6\right)=25 x^{2}-30 x+9
$$

or

$$
21 x^{2}-58 x-15=0
$$

from which

$$
x_{1}=3, x_{2}=-\frac{5}{21}
$$

1

(Jeczuskó Imre, Eperjes.)[^0]


[^0]:    ${ }^{1}$ The second root is false, because the left side is positive, while the right side is negative