Question

The number of natural number n for which the equation (x-8)x=n(n-10) has no real solution is

Answer 1

Step-by-step explanation:

Given The number of natural number n for which the equation                    (x-8) x = n (n-10) has no real solution is

• We need to find the number of natural number n.
• So we have (x – 8) x = n (n – 10)
• So x^2 – 8x = n^2 – 10 n
• Now x^2 – 8x – n^2 – 10 n will not have any solution
• Now if 8^2 – 4(10 n – n^2) < 0
• So 64 – 40 n + 4n^2 < 0
• So 4(16 – 10 n + n^2) < 0
• So – n^2 – 10 n - 16 < 0
• Or n^2 + 10 n + 16 < 0
• Or n^2 – 8n – 2n + 16 < 0
• Or n(n – 8) – 2(n – 8) < 0
• Or (n – 8) (n – 2) < 0
• Or 2 < n < 8
• So n can have the values 3,4,5,6,7
• Therefore for n = 3,4,5,6,7,10 has no solution for x

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https://brainly.in/question/17685678