Find the sum of a+b+c+d

Algebra Level 2

find the answer for the above condition


The answer is 105.

Anand Shah by Anand Shah , 22, India

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2 solutions

Danton Libunao
Mar 7, 2014

27x^3 - 512y^3 = (3x - ay) (bx^2 + cxy +dy^2 factor 27x^3 -512y^3 then we get, (3x - 8y) (9x^2 + 24xy + 64y^2) = (3x - ay) (bx^2 +cxy + dy^2) from the equation above we simply get the value of a, b, c & d. so; a + b + c + d = 8 + 9 + 24 + 64 = 105

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Sarthak Tanwani
Mar 26, 2014

it resembles the identity, <marquee> a^3 - b^3 = ( a - b ) ( a^2 + b^2 + ab ) <marquee/> <marquee> So we can directly put the values and get, <marquee/> <marquee> 27x^3 - 512y^3 = (3x)^3 - (8y)^3 = ( 3x - 8y )[ (3x)^2 + (8y)^2 + (3x)(8y)] = ( 3x - 8y )(9x^2 + 64y^2 + 24xy) <marquee/> <marquee> So,a=8, b=9, c=24, d=64 <marquee/> <marquee> a+b+c+d = 8+9+24+64 = 105 <marquee/>

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