Question

If x³ - y³ = 26 and x⁴ -y⁴ = 20(x+y) find the values of x and y .​

Answer 1

Step-by-step explanation:

Let x²-3x = y.

Then, y² - 8y - 20

= y² - 10y + 2y - 20

= y (y-10) + 2 (y-10)

= (y-10) (y+2)

= (x²-3x-10) (x²-3x+2) [Putting the value]

= (x²-5x+2x-10) (x²-2x-x+2)

= [x(x-5)+2(x-5)] [x(x-2)-1(x-2)]

= (x-5) (x+2) (x-2) (x-1) [ANSWER]

Answer 2

Answer:

Step-by-step explanation:

Let x²-3x = y.

Then, y² - 8y - 20

= y² - 10y + 2y - 20

= y (y-10) + 2 (y-10)

= (y-10) (y+2)

= (x²-3x-10) (x²-3x+2) [Putting the value]

= (x²-5x+2x-10) (x²-2x-x+2)

= [x(x-5)+2(x-5)] [x(x-2)-1(x-2)]

= (x-5) (x+2) (x-2) (x-1) [ANSWER]