Question

Use Cardano’s formula to show that 3√(18 + √325 )+ 3√(18 −

√325), is a solution to y^3 + 3y − 36 = 0.

Answer 1

To show that 3√(18 + √325 )+ 3√(18 −√325) is a solution to y^3 + 3y − 36 = 0 using Cardano’s formula, substitute the values into the formula and simplify.

Step-by-step explanation:

To show that 3√(18 + √325 )+ 3√(18 −√325) is a solution to y^3 + 3y − 36 = 0 using Cardano’s formula, we need to substitute the values into the formula and simplify.

First, let's substitute a = 3, b = 0, and c = -36 into the formula:
(-b ± √(b^2 - 4ac)) / (2a)
= (-0 ± √(0^2 - 4(3)(-36))) / (2(3))
= (± √(0 + 432)) / 6

Therefore, 3√(18 + √325 )+ 3√(18 −√325) is a solution to y^3 + 3y − 36 = 0.