Question

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

Answer 1

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

Answer 2

Solution

Step-by-step explanation:

The equation is $x^3+y^3+15xy-125$

Given,

$x+y=5$

So, you know that  $x^3+y^3=(x+y)^3-3xy(x+y)$

Then, put the value of  $x^3+y^3$ in equation,

$(x+y)^3-3(x+y)+15xy-125$

Then, put the value of $x+y$ that is given in the question,

$(5)^3-3xy(5)+15xy-125$

$125-15xy+15xy-125$ $=0$

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