Mathematics: What is the solution of square root 1-3x = x+3

What is the solution of square root 1-3x = x+3 - id1334950844, chocolate12377

22nathanieltimms

17.01.2022

ANSWER

x = - 1

EXPLANATION

The given equation is

$\sqrt{ 1 - 3 x} = x + 3$

Square both sides to get,

$1 - 3x = {(x + 3)}^{2}$

Expand:

$1 - 3x = {x}^{2} + 6x + 9$

${x}^{2} + 6x + 3x + 9 - 1 = 0$

${x}^{2} + 9x + 8 = 0$

${x}^{2} + 8x + x + 8 = 0$

x(x + 8) + 1(x + 8) = 0

(x + 1)(x + 8) = 0

$x = - 1 \: or \: x = - 8$

Check for extraneous solutions.

When x=-1, we put x=-1 into the original equation:

$\sqrt{ 1 - 3 ( - 1)} = - 1+ 3$

$\sqrt{ 1 +3 } = 2$

$\sqrt{ 4 } = 2$

2 = 2

This is true.

Also check for x=-8.

$\sqrt{ 1 - 3 ( - 8)} = - 8+ 3$

$\sqrt{ 25} = -5$

$5 \ne - 5$

This is an extraneous solution.

Hence x=-1 is the only solution.

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