15 = 4 + 3w²

15 = 4 + 3w²

Question
\(\displaystyle{15}={4}+{3}{w}²\)

Answers (1)

2021-02-05
We are given: \(\displaystyle{15}={4}+{3}{w}²\)
Subtract 4 from both sides: \(\displaystyle{11}={3}{w}²\)
Divide both sides by 3: \(\displaystyle\frac{{11}}{{3}}={w}²\)
Take the square root of both sides:
\(\displaystyle\pm{\left(\sqrt{{\frac{{11}}{{3}}}}\right)}={w}\)
or
\(\displaystyle{w}=\pm\frac{\sqrt{{11}}}{\sqrt{{3}}}\)
Rationalize: \(\displaystyle{w}=\pm{\left(\frac{\sqrt{{11}}}{\sqrt{{3}}}\right)}\cdot{\left(\frac{\sqrt{{3}}}{\sqrt{{3}}}\right)}\) \(\displaystyle{w}=\pm\frac{\sqrt{{33}}}{{3}}\)
0

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