Question

√6 * х=( √(2⁵ * 18) ) / ∛6

Answer 1

Дано уравнение √6*х = (√(2⁵*18)) / ∛6.

Отсюда переменная х находится прямо:

х = (√(2⁵ * 18) ) /(∛6*√6)  = (√(2⁵ * 2*9) ) / (6^((1/3)+(1/2)) = (2³*3)/6^(5/6) =

 = 24/6^(5/6) = (24*6^(1/6))/(6^(5/6)*6^(1/6)) = (24*6^(1/6))/6 = 4*6^(1/6) ≈ 5,392025.

Answer 2

To solve the equation √6 * x = (√(2⁵ * 18)) / ∛6, we need to find the value of 'x'. Let's break down the steps to solve the equation:

Step 1: Simplify the right-hand side of the equation.

√(2⁵ * 18) = √(32 * 18) = √576 = 24

Step 2: Simplify the denominator on the right-hand side of the equation.

∛6 = 6^(1/3)

Step 3: Now, we can rewrite the equation as follows:

√6 * x = 24 / (6^(1/3))

Step 4: To isolate 'x', divide both sides of the equation by √6.

x = (24 / (6^(1/3))) / √6

Step 5: Rationalize the denominator on the right-hand side.

To rationalize the denominator (remove the square root), we need to multiply both the numerator and denominator by √6.

x = (24 / (6^(1/3))) * (1 / √6)

Step 6: Simplify the expression in the numerator.

The cube root of 6 (6^(1/3)) is the same as 6 raised to the power of (1/3), which is equal to 6^(1/3) = 2.

x = (24 / 2) * (1 / √6)

Step 7: Continue simplifying.

x = 12 * (1 / √6)

Step 8: Rationalize the denominator again.

To rationalize the denominator, multiply both the numerator and denominator by √6.

x = 12 * (1 / √6) * (√6 / √6)

Step 9: Simplify the expression.

x = 12 * √6 / 6

Finally, the value of 'x' is:

x = 2√6

Therefore, the solution to the equation is x = 2√6.