Question

^3√х+4=6 математика Математика

Answer 1

Возводим уравнение в куб:
x+4=216
x=216-4
x=212

Answer 2

To solve the equation ^3√(х + 4) = 6 for x, we need to isolate the variable x. Here's the step-by-step solution:

Step 1: Subtract 4 from both sides of the equation to get rid of the constant term on the left side: ^3√(x + 4) - 4 = 6 - 4

Step 2: Simplify both sides: ^3√(x + 4) - 4 = 2

Step 3: Now, cube both sides to eliminate the cube root on the left side: (^3√(x + 4) - 4)^3 = 2^3

Step 4: Simplify both sides: x + 4 - 4*^3√(x + 4) + 6*√(x + 4)^2 - 4^3 = 8

Step 5: Simplify further using the formula (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3: x + 4 - 34^2√(x + 4) + 34^2√(x + 4)^2 - 4^3 = 8

Step 6: Simplify the terms with square roots: x + 4 - 48*√(x + 4) + 192 - 64 = 8

Step 7: Combine like terms: x - 60*√(x + 4) + 128 = 8

Step 8: Move the constant term to the right side of the equation: x - 60*√(x + 4) = 8 - 128

Step 9: Simplify the right side: x - 60*√(x + 4) = -120

Step 10: Add 60√(x + 4) to both sides to isolate x: x = -120 + 60√(x + 4)

Now, the equation is in a simplified form, but it cannot be easily solved algebraically. To find the numerical value of x, you might need to use numerical methods or graphing techniques.