Let a, b, c, p be rational numbers such that p is not a perfect cube.a+bp13+cp23=0, then prove that

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Let a,b,c,p be rational numbers such that p is not a perfect cube. a plus b p power one by three plus plus c p power two by three is equal to zero then prove that a equal to b equal to c equal to zero
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Class 10 Real Numbers is a foundational mathematics course that introduces students to the fundamental concepts of real numbers, laying the groundwork for more advanced mathematical studies. This course typically covers topics such as:

Introduction to Real Numbers: Students learn about the basic properties of real numbers, including their classification as rational or irrational.

Rational Numbers: This section delves into rational numbers, which can be expressed as the quotient of two integers. Students learn operations such as addition, subtraction, multiplication, and division of rational numbers.

Irrational Numbers: Students are introduced to irrational numbers, which cannot be expressed as the quotient of two integers. They learn about famous irrational numbers such as π (pi) and √2 (square root of 2).

Properties of Real Numbers: This part focuses on the properties of real numbers, including closure, commutativity, associativity, distributivity, and the existence of additive and multiplicative identities and inverses.

Representation of Real Numbers on Number Line: Students learn how to represent real numbers on a number line, gaining an intuitive understanding of the ordering and magnitude of different numbers.

Decimal Representation of Rational Numbers: Students explore decimal representation of rational numbers and learn about recurring and terminating decimals.

Euclid’s Division Lemma and Algorithm: This section introduces students to Euclid’s Division Lemma and Algorithm, which are fundamental tools for understanding the properties of integers.

Fundamental Theorem of Arithmetic: Students learn about the Fundamental Theorem of Arithmetic, which states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers, and this representation is unique.

Application of Real Numbers: Students apply their understanding of real numbers to solve various mathematical problems and real-world scenarios.

Overall, Class 10 Real Numbers provides students with a solid foundation in the properties and operations of real numbers, equipping them with essential mathematical skills for future academic and practical endeavors.

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Sir jab apna p⅓ sa multiply kiya tab 0×p⅓ to ak irrational no. Ho jayaga na kyoki 0 rational???

RajdeepKalita-vg