Answer:
Option D. {1,-17}
Step-by-step explanation:
n^2+16n=17
n^2+16n+(16/2)^2=17+(16/2)^2
n^2+2n(8)+(8)^2=17+(8)^2
(n+8)^2=17+64
(n+8)^2=81
sqrt[(n+8)^2]=+-sqrt(81)
n+8=+-9
n+8-8=+-9-8
n=+-9-8
n1=+9-8→n1=1
n2=-9-8→n2=-17
Solution: {1,-17}
Option D is correct, i.e. {1, -17}.
Given the problem is n² + 16n = 17.
Comparing it with general form of Perfect Square i.e. x² + 2ax + a² = (x+a)².
We can write it as follows:-
n² + 2*8n = 17
Adding 8² on both sides,
n² + 2*8n + 8² = 17 + 8²
(n+8)² = 17 + 64 = 81
n+8 = √81 = ±9
n+8 = 9 or n+8 = -9
n = 9-8 or n = -9-8
n = 1 or n = -17
Hence, option D is correct, i.e. {1, -17}.
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