Find the exact solution for each equaton. Find the approximate solution to the nearest tenth.
3 sq rt 3/sq rt 1 + sq rt 1 = x/sq rt 3
Please solve and explain. Thanks
To solve this equation, we need to isolate the variable x. Let's break down the steps:
Step 1: Simplify the equation
The square root of 1 is 1, so we can simplify the equation as follows:
3√3 / √1 + √1 = x / √3
3√3 / 1 + 1 = x / √3
3√3 / 2 = x / √3
Step 2: Multiply both sides by √3
Multiply both sides of the equation by the square root of 3 to eliminate the square roots:
(3√3 / 2) * √3 = (x / √3) * √3
(3√3 / 2) * √3 = x
Step 3: Simplify the left side
To simplify the left side, we need to multiply the fraction and square root:
(3√3 / 2) * √3 = (3√3 * √3) / 2
(3√3 / 2) * √3 = (3 * 3) / 2
(3√3 / 2) * √3 = 9 / 2
Therefore, the exact solution is x = 9/2
To find the approximate solution to the nearest tenth, we can consider the decimal equivalent of the fraction 9/2, which is 4.5. Therefore, the approximate solution is x = 4.5.
Note: The exact solution is given as a fraction, while the approximate solution is given as a decimal to the nearest tenth.