let a b c and p be rational numbers such that p is not a perfect cube. if a+bp at the power 1/3=0 prove a=b=c=0
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a, b, c and p are rational. p is not a perfect cube. so p¹/³ and p²/³ are not rational numbers. Then p is not 1 or 0.p²/³ = p¹/³ * p¹/³ and so they are not equal.
LHS = a + b p¹/³ + c p²/³ = 0 --- (1) Given p is not a perfect cube. p is not 0 or 1. Also are irrational. Multiply (1) by p^1/3 to get: Substitute the value of c in (1) to get: So p^1/3 is imaginary. It is a contradiction as p is a rational number. Given quadratic isn't valid. So a = b = c = 0. There is alternate method to solve it. See the enclosed picture.
Read more on Brainly.in - https://brainly.in/question/379335#readmore
LHS = a + b p¹/³ + c p²/³ = 0 --- (1) Given p is not a perfect cube. p is not 0 or 1. Also are irrational. Multiply (1) by p^1/3 to get: Substitute the value of c in (1) to get: So p^1/3 is imaginary. It is a contradiction as p is a rational number. Given quadratic isn't valid. So a = b = c = 0. There is alternate method to solve it. See the enclosed picture.
Read more on Brainly.in - https://brainly.in/question/379335#readmore
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