Question

If x - y = 2 and xy = 8, then find the value
of x^3 – y^3.​

Answer 1

Given

we have given x-y= 2

and xy=8

To Find

we have to find the value of x³-y³

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

X-y= 2

X= 2+y----(1)

Now , xy= 8

from equation 1 put X's value into this equation

=>(2+y)y=8

=>2y+y²=8

=>y²+2y=8

=>y²+2y-8=0

Now,it is in the form of a quadratic equation so we simply factorise it.

=>y²+4y-2y-8=0

=>y(y+4)-2(y+4)=0

=>(y-2)(y+4)=0

y-2=0

y=2

y+4=0

y=-4

from equation 1

x= 2+y

=>x= 2+2 or x= 2+(-4)

=>x=4 or x= -2

We have x= 4 & x= -2

and y = 2 & y= -4

We have to find x³-y³

At x = 4 & y = 2

x³-y³= (4)³-(2)³=64-8=56

At x= -2 & y= -4

x³-y³= (-2)³-(-4)³=-8-(-64)=-8+64=56

Hence, value of x³-y³ is 56.