If x- y = \(\sqrt {5}\)
10 + xy = \(\frac{13}{xy}\)
find x4 + y4 + 10
Answer & explanation
Correct answer: option 2
x- y = \(\sqrt {5}\)
x2 + y2 = 5 + 2xy
x4 + y4 = 25 + 4x2y2 + 20xy - 2x2y2
x4 + y4 = 25 + 2x2y2 + 20xy
= 25 + 2xy(xy + 10)
= 25 + 2xy × \(\frac{13}{xy}\)
x4 + y4 = 51
x4 + y4 +10 = 61