Given that $sqrt(x^2+4)=-3x$ determine the value or values of $x$ ?

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Answer 1 · 2016-06-27T13:34:08

$x=+-sqrt(2)/2$

The x-intercept is at $y=0$

Write as: $" "0=3x-sqrt(x^2+4)$

Add $sqrt(x^2+4)" "$ to both sides

$sqrt(x^2+4)=3x$

Square both sides

$x^2+4=9x^2$

Subtract $" "x^2$ from both sides

$8x^2=4$

Divide both sides by 8

$x^2=1/2$

Square root both sides

$x=+-1/sqrt(2)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mathematicians consider it bad practice to have roots in the denominator if at all avoidable.

Multiply b1 but in the form of $1=sqrt(2)/ sqrt(2)$

$x=+-1/sqrt(2)xxsqrt(2)/ sqrt(2) = +-sqrt(2)/2$

Given that sqrt(x^2+4)=-3xsqrt(x^2+4)=-3x determine the value or values of xx?