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, 9 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 5 years, 9 months ago

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

1Thank You

Om Singh 5 years, 9 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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CBSE > Class 09 > Mathematics