Question

7. If x + y = 9 and xy = 8, then what is one of the values of (x power 4-y power 4)
​(a)4025 (b)4095

Answer 1

option b is right

x^4 - y^4 = (x²+y²)(x²- y²). . ...(1)

x+y = 9.....(2)

squaring on both sides

x²+y² +2xy = 81

x²+y² = 81-2xy = 81- 16 = 65

x²+y²= 65☑

now , (x-y)² = x²+y² - 2xy

( x-y)² = 65-2×8 = 65-16 = 49

x-y = 7.....(3)

by adding (2) and (3)

2x = 16 => x = 8☑

put it in (2)

x+y = 9

y= 9-x = 9-8 = 1☑

put these values in (1)

we get,

x^4 - y^4 = 65×(64-1)

= 65×63

= 4095

hence option b is ryt