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

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Answer 1 · 2016-08-19T13:47:31

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

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

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

$\Rightarrow x^{2} - 17 x + 42 = 0$ $rArr x^2-17x+42=0$ .

Using, $14 \times 3 = 42, and, 14 + 3 = 17$ $14xx3=42, and, 14+3=17$ , 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−√3x+7=7x- sqrt(3x + 7) = 7?