Sum of all values of n ∈ N for which the equation (x-8/n-10)=(n/x) has no solution, equals

Question

Sum of all values of n ∈ N for which the equation (x-8/n-10)=(n/x) has no solution, equals (A) 25 (B) 35 (C) 20 (D) 40

Tardigrade Admin · Accepted Answer

x 2-8 x -( n 2-10 n )=0 D =64+4( n 2-10 n )< 0 n 2-10 n +16< 0 ( n -8)( n -2)< 0 n ∈(2,8) text also ( n =10 text Sum of all values of n =3+4+5+6+7+10=35

Q. Sum of all values of $n \in N$ for which the equation $\frac{x - 8}{n - 10} = \frac{n}{x}$ has no solution, equals

25

35

20

40

$x^{2} - 8 x - (n^{2} - 10 n) = 0$
$D = 64 + 4 (n^{2} - 10 n) < 0$
$n^{2} - 10 n + 16 < 0$
$(n - 8) (n - 2) < 0$
$n \in (2, 8) also (n = 10$
$Sum of all values of n = 3 + 4 + 5 + 6 + 7 + 10 = 35$

Q. Sum of all values of n∈N for which the equation n−10x−8​=xn​ has no solution, equals

25

35

20

40

x2−8x−(n2−10n)=0 D=64+4(n2−10n)<0 n2−10n+16<0 (n−8)(n−2)<0 n∈(2,8) also (n=10 Sum of all values of n=3+4+5+6+7+10=35

Q. Sum of all values of $n \in N$ for which the equation $\frac{x - 8}{n - 10} = \frac{n}{x}$ has no solution, equals

$x^{2} - 8 x - (n^{2} - 10 n) = 0$
$D = 64 + 4 (n^{2} - 10 n) < 0$
$n^{2} - 10 n + 16 < 0$
$(n - 8) (n - 2) < 0$
$n \in (2, 8) also (n = 10$
$Sum of all values of n = 3 + 4 + 5 + 6 + 7 + 10 = 35$