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Which are the roots of [tex]\( 81x^2 = 144 \)[/tex]?

A. [tex]\( x = \pm \frac{4}{3} \)[/tex]
B. [tex]\( x = -1 \)[/tex]
C. [tex]\( x = \frac{4}{3} \)[/tex]
D. [tex]\( x = \pm 1 \)[/tex]

Sagot :

GinnyAnswer
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]
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