Question

find the value of 27xcube+8ycube, if. 3x+2y=14 and xy=8

Answer 1

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Answer 2

Heya!!

3x + 2y = 14 ( Given)

xy = 8 ( Given)

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( 3x+2y)^2 = (14)^2

=) (3x)^2 + (2y)^2 + 2 (3x)(2y) = 196

=) 9x^2 + 4y^2 + 12xy = 196

=) 9x^2 + 4y^2 + 12 (8) = 196

=) 9x^2 + 4y^2 = 196 - 96

=) 9x^2 + 4y^2 = 100

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Now,

27x^3 + 8y^3

= (3x)^3 + (2y)^3

Since, a^3 + b^3 = (a+b)(a^2 + b^2 + ab)

= ( 3x + 2y) {( 3x)^2 + (2y)^2 + (3x)(2y) }

= (3x+2y) ( 9x^2 + 4y^2 - 6xy)

= (14) ( 100 - 6 (8) )

= 14 × 52

= 728

Hope it helps u :)