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Show That: `(X^(A^2+B^2)/X^(Ab))^(A+B)(X^(B^2+C^2)/X^(Bc))^(B+C)(X^(C^2+A^2)/X^(Ac))^(A+C)=X^(2(A^3+B^3+C^3))` - CBSE Class 9 - Mathematics

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Question

Show that:

`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`

Solution

`(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))`

LHS = `(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)`

`=(x^(a^2+b^2-ab))^(a+b)(x^(b^2+c^2-bc))^(b+c)(x^(c^2+a^2-ac))^(a+c)`

`=[x^((a+b)(a^2+b^2-ab))][x^((b+c)(b^2+c^2-bc))][x^((a+c)(c^2+a^2-ac))]`

`=(x^(a^3+b^3))(x^(b^3+c^3))(x^(a^3+c^3))`

`=x^(2(a^3+b^3+c^3))`

= RHS

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.20 | Q: 4.4 | Page no. 25

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Solution Show That: `(X^(A^2+B^2)/X^(Ab))^(A+B)(X^(B^2+C^2)/X^(Bc))^(B+C)(X^(C^2+A^2)/X^(Ac))^(A+C)=X^(2(A^3+B^3+C^3))` Concept: Laws of Exponents for Real Numbers.
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