To find the roots of the equation [tex]\(81x^2 = 144\)[/tex], let's follow a step-by-step solution:
1. Start with the given equation:
[tex]\[
81x^2 = 144
\][/tex]
2. Divide both sides of the equation by 81 to isolate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 = \frac{144}{81}
\][/tex]
3. Simplify the fraction on the right-hand side:
[tex]\[
x^2 = \frac{16}{9}
\][/tex]
4. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm \sqrt{\frac{16}{9}}
\][/tex]
5. Simplify the square root:
[tex]\[
x = \pm \frac{4}{3}
\][/tex]
Thus, the roots of the equation [tex]\(81x^2 = 144\)[/tex] are [tex]\(x = \frac{4}{3}\)[/tex] and [tex]\(x = -\frac{4}{3}\)[/tex].
So, the correct answer is:
[tex]\[ x = \pm \frac{4}{3} \][/tex]
