Question

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

Answer 1

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

Explanation:

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)`
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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`