Question
Question: The no. of real roots of (6 – x)<sup>4</sup> + (8 – x)<sup>4</sup> = 16 is-...
The no. of real roots of (6 – x)4 + (8 – x)4 = 16 is-
A
0
B
2
C
4
D
None of these
Answer
2
Explanation
Solution
y = 7 – x
(y–1)4 + (y + 1)4 = 16
Ž y4 + 6y2 – 7 = 0 Ž y2 – 1 = 0
Ž y = ± 1
7 – x = 1 Ž x = 6
7 – x = – 1 Ž x = 8