How do you solve $x- sqrt(3x + 7) = 7$ ?

Question

2754 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-19T13:47:31

The soln. is $x=14$ , and, $x=3$ is extraneous soln..

Rewriting the eqn. as, $x-7=sqrt(3x+7)$ , and, squaring, we get,

$x^2-14x+49=3x+7$ .

$rArr x^2-17x+42=0$ .

Using, $14xx3=42, and, 14+3=17$ , we have,

$ul(x^2-14x)-ul(3x+42)=0$ .

$rArr x(x-14)-3(x-14)=0$ .

$rArr (x-14)(x-3)=0$ .

$rArr x=14, or, x=3$ .

Recall that $sqrt(3x+7)$ is always $+ve$ , so that, $x=3$ does not satisfy the original eqn., &, hence is an extraneous soln.

Thus, the soln. is $x=14$ , and, $x=3$ is extraneous.

How do you solve x- sqrt(3x + 7) = 7x- sqrt(3x + 7) = 7?