Question

if X^3+y^3=25and x+y=5 than find out the x^4+y^4

Answer 1

Answer:

425/9

Step-by-step explanation:

x³ + y³ = 25 and x+y = 5;

(x³+y³)(x+y) = x⁴ + xy³+yx³+y4 = x⁴ + y⁴ + xy(x²+y²)

we need to find values of xy and x²+y²

cubing x+y = 5 to get value of xy;

(x+y)³ = 125 =>  x³+y³+3xy(x+y) = 125 => 25 + 3xy(5) = 125

=> 15xy = 100 => xy = 100/15 = 20/3.

Squaring x+y = 5 to get value of x² + y²

(x+y)² = 25

x²+ y²+2xy = 25

x² + y² = 25 - 2xy = 25 - 2*20/3 = 25 - 40/3 = 35/3.

Now substitute the values back

=> 25 * 5 = x⁴ + y⁴ + xy(x²+y²)

=> 125 =  x⁴ + y⁴ + 20/3*35/3

x⁴ + y⁴  = 125 - 700/9 = 1125 - 700/9 = 425/9