If x + y = 10, product of x and y is 16, then the value of x⁴ + y⁴ is:

Correct option is D

​Given:

x + y = 10

xy = 16

We need to find the value of  $$x^4 + y^4$$​​

Formula Used:

​$$x^2 + y^2 = (x + y)^2 - 2xy$$​​

​$$x^4 + y^4 = (x^2 + y^2)^2 - 2(xy)^2$$​​

Solution:

​$$x^2 + y^2 = (x + y)^2 - 2xy = 10^2 - 2 \times 16 = 100 - 32 = 68$$​​

Now, 

$$x^4 + y^4 = (x^2 + y^2)^2 - 2(xy)^2$$​​

​$$x^4 + y^4 = 68^2 - 2 \times 16^2$$​​

= 4624 - 2 $$\times$$​ 256 = 4624 - 512 = 4112

Thus, the value of $$x^4 + y^4$$​ is 4112

Alternate Solution: ​

taking x = 8 and y = 2 

x + y = 8 +2 = 10 (satisfies), 

x$$\times$$y = 8 ×2 = 16 (satisfies) 

Now, x⁴+ y⁴ 

= (8)⁴ + (2)² = 4096 + 16 = 4112
​