Question

7. If x + y = 9 and xy = 8, then what is one of the values of (x4 - y4)
(a) 4025
(b).4065
(c) 4095
(d)4905
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Answer 1

Answer is Option c)4095.

Given: x+y=9--(1) and xy=8=>x=8/y--(2)

Substituting (2) in (1),

(8/y)+y=9

=>8+y^2=9y

=>y^2-9y+8=0

=>y=1 or 8

=>x=8 or 1

Here x=8 and y=1 is correct because the answer would be negative in the other case.

Therefore substituting x=8 and y=1 in x^4-y^4,

=8^4-1^4

=4096-1

=4095.

Answer 2

x+y=9

x y=8

x=8/y

then substiting x value

8/y+y=9

8+y2/y=9

8+y2=9y

cancelled of y

8+y=9

y=9-8

y=1

x=8/y=8/1

$x {}^{4 } - y {}^{4} = {8}^{4} - 1 {}^{4}$

4096-1=4095

4095 is a correct answer.