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# If X/A = Y/B = Z/C Prove that (2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3 - ICSE Class 10 - Mathematics

#### Question

If x/a = y/b = z/c prove that (2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3

#### Solution

Let x/a = y/b = z/c = k

Then x = ak, y = bk and z = ck

L.H.S = (2x^3 - 3y + 4z)/(2a^3 - 3b^3 + 4c^3)

= (2(ak)^3 - 3(bk)^3 + 4(ck)^3)/(2a^3 - 3b^3 + 4c^3)

= (k^3(2a^3 - 3b^3 + 4c^2))/(2a^3 - 3b^3 + 4c^3)

= k^3

RHS = ((2x - 3y + 4z)/(2a - 3b + 4c))^3

= ((2ak - 3bk + 4ck)/(2a - 3b + 4c))^3

= [(k(2a - 3b + 4c))/(2a - 3b + 4c)]^3

= k^3

Hence LHS = RHS

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7B | Q: 20

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Solution If X/A = Y/B = Z/C Prove that (2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3 Concept: Proportions.
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