Question

if 5x + 3y= 16 and xy= 2. Find the value of 125x cube + 27y cube​

Answer 1

Answer:

125x³+27y³=2656

Step-by-step explanation:

5x+3y=16

Cubing on both the sides

(5x+3y)³=(16)³

(5x)³+(3y)³+3(5x)(3y)(5x+3y)=4096

125x³+27y³+(45xy)(16)=4096

125x³+27y³+(45)(2)(16)=4096

125x³+27y³+1440=4096

125x³+27y³=4096-1440

125x³+27y³=2656

Answer 2

Given : 5x + 3y= 16 and xy= 2.

To Find :  Value of  125x³ + 27y³

Solution:

(a + b)³ = a³ + b³  + 3ab(a + b)

5x + 3y= 16

Taking cube both sides

=> (5x + 3y)³   = 16³

=> 125x³ + 27y³  + 3(5x)(3y)(5x + 3y)  = 16³

=>  125x³ + 27y³  + 45xy(5x + 3y)  = 16³

5x + 3y= 16   and xy = 2

=>  125x³ + 27y³  + 45(2)(16)  = 16³

=> 125x³ + 27y³  + 90(16)  = 16³

=> 125x³ + 27y³  = 16³ -    90(16)

=>  125x³ + 27y³  = 16 ( 16² - 90)

=> 125x³ + 27y³  = 16 (256 - 90)

=>  125x³ + 27y³  = 16 (166)

=> 125x³ + 27y³  = 2656

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