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2x+3y proportional 3x-4y then prove x 3 +y 3 proportional xy(x+y)

2x+3y proportional 3x-4y then prove 
x3+y3 proportional xy(x+y)

Grade:10

1 Answers

Saumen Ghosh
13 Points
2 years ago
2x+3y proportional to 3x-4y
or, 2x+3y = k(3x-4y) [ k = proportionality constant ]
or, (3k-2)x = (4k+3)y
or, x = (4k+3)/(3k-2) .y
or, x=my [m= (4k+3)/(3k-2) ]
 
Now, x^3-y^3/xy(x-y)
= (x-y)(x^2-xy+y^2)/xy(x-y)
= (x^2-xy+y^2)/xy
= (m^2.y^2 - m.y^2 + y^2)/ m^2. y^2
= (m^2-m+1)/m^2
= n (let)
Therefore, x^3-y^3 proportional to xy(x-y)
 

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