Question
solve the following equations and include simple step by step instructions
-x^3/2 = -27
x = _
27x^3/4 - 1 = 26
x = _
-x^3/2 = -27
x = _
27x^3/4 - 1 = 26
x = _
Answers
Answered by
GPT-5 mini
1) -x^3/2 = -27
Step 1: Multiply both sides by -2 to clear the fraction and sign:
x^3 = 54
Step 2: Take the cube root of both sides:
x = ∛54 = 3∛2 ≈ 3.779763
So x = 3∛2 (≈ 3.7798).
2) 27x^3/4 - 1 = 26
Step 1: Add 1 to both sides:
(27x^3)/4 = 27
Step 2: Multiply both sides by 4:
27x^3 = 108
Step 3: Divide by 27:
x^3 = 4
Step 4: Take the cube root:
x = ∛4 = 2^(2/3) ≈ 1.587401
So x = ∛4 (≈ 1.5874).
Step 1: Multiply both sides by -2 to clear the fraction and sign:
x^3 = 54
Step 2: Take the cube root of both sides:
x = ∛54 = 3∛2 ≈ 3.779763
So x = 3∛2 (≈ 3.7798).
2) 27x^3/4 - 1 = 26
Step 1: Add 1 to both sides:
(27x^3)/4 = 27
Step 2: Multiply both sides by 4:
27x^3 = 108
Step 3: Divide by 27:
x^3 = 4
Step 4: Take the cube root:
x = ∛4 = 2^(2/3) ≈ 1.587401
So x = ∛4 (≈ 1.5874).