1.

What is the value of x cube + y cube +15xy -125 if x+y =5

Answer»

Answer:

0

Step-by-step explanation:

Given-----> x + y = 5

To find-----> x³ + y³ + 15 xy - 125

Solution-----> We know that,

If , p + q + r = 0 , then ,

p³ + q³ + r³ = 3pqr

Now , returning to original PROBLEM,

ATQ, x + y = 5

=> x + y - 5 = 0

=> x + y + ( - 5 ) = 0 .................( 1 )

Now ,

x³ + y³ + 15xy - 125

= ( x )³ + ( y )³ - 125 + 15 xy

= ( x )³ + ( y )³ + ( -125 ) - ( - 15 ) x y

= ( x )³ + ( y )³ + ( -5 )³ - 3 ( x ) ( y ) ( - 5 ) ...............( 2 )

Now , Let ,

p = x , q = y , r = ( - 5 )

Now PUTTING these values in ( 1 ) , we GET,

p + q + r = 0

Now putting in ( 2 ) we get,

x³ + y³ + 15 xy - 125 = p³ + q³ + r³ - 3pqr

Now applying above identity , we get,

x³ + y³ + 15xy - 125 = 3pqr - 3pqr

=> x³ + y³ + 15xy - 125 = 0



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