find the equations whose roots are the cubes of the roots of x³+3x²+2=0 ?
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Step-by-step explanation:
Given equation is x3 + 3x2 + 2 = 0
Put y = x3 so that x = y1/3
∴ y + 3y2/3 + 2 = 0 3y2/3 = – (y + 2)
Cubing on both sides,
27y2 = – (y + 2)3 = – (y3 + 6y2 + 12y + 8) ∴ y3 + 6y2 + 12y + 8 = 0 ⇒ y3 + 33y2 + 12y + 8 = 0
Required equation is x3 + 33x2 +12x +8= 0
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