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If 2x+3y=12andxy=16 then find 8x3+27y3

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If 2x+3y=12andxy=16 then find 8x3+27y3

    • Posted by Om Singh 5 years, 3 months ago

    CBSE > Class 09 > Mathematics
    • 2 answers

    Sia ? 5 years, 3 months ago

    We have,
    (2x + 3y) = 13
    {tex}\Rightarrow{/tex} (2x + 3y)3 = 133
    {tex}\Rightarrow{/tex} (2x)3 + (3y)3 + 3 {tex}\times{/tex} 2x {tex}\times{/tex} 3y(2x + 3y) = 133
    {tex}\Rightarrow{/tex} 8x3 + 27y3 + 18xy(2x + 3y) = 2197
    {tex}\Rightarrow{/tex} 8x3 + 27y3 + 18 {tex}\times{/tex} 6 {tex}\times{/tex} 13 = 2197
    {tex}\Rightarrow{/tex} 8x3 + 27y3 + 1404 = 2197
    {tex}\Rightarrow{/tex} 8x3 + 27y3 = 2197 - 1404 = 793

    1Thank You

    Om Singh 5 years, 3 months ago

    (2x+3y)³=2x³+3y³+3*2x*3y(2x+3y) =(12)². After putting value of 2x+3y andxy so 8x³+27y³+18*6 *12=1728. 8x³+27y³=1728-1296. So. 8x³+27y³=432

    1Thank You

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