Mathematics Questions and Answers

1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\)

sum of roots - \(1 + \sqrt{13} + 1 - \sqrt{13} = 2\)

Product of roots = (1 - \(\sqrt{13}\)) (1 + \(\sqrt{13}\)) = -12

x2 - (sum of roots) x + (product of roots) = 0

x2 - 2x - 12 = 0

f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4

= (2 + 3) (x - 3) + 4

= 5(x - 3) + 4

= 5x - 15 + 4

= 5x - 11

f(3) = 5 x 3 - 11

= 4

g(f(3)) = g(4)

= \(\sqrt{5 + 4}\)

= \(\sqrt{9}\)

= 3

g(4) = 3

f(g(4)) = f(3)

= 4

g[f(3)] and f[g(4)] = 3 and 4 respectively.

Tunde and Shola can do the work in 18 days.

Both will do the work in \(\frac{1}{18}\) days.

But Tunde can do the whole work in x days; Hence he does \(\frac{1}{x}\) of the work in 1 day.

Shola does the work in (x + 15) days; hence, he does \(\frac{1}{x + 15}\) of the work in 1 day.

\(\frac{1}{x} + \frac{1}{x + 15} = \frac{1}{18}\)

\(\frac{2x + 15}{x^{2} + 15x} = \frac{1}{18}\)

\(x^{2} + 15x = 36x + 270\)

\(x^{2} + 15x - 36x - 270 = 0\)

\(x^{2} - 21x - 270 = 0\)

2x + 3y = 1 x 2.......(i) x - 2y = 11 x 3.......(ii) 4x + 6y = 2........(iii) 3x - 6Y = 33........(4) 7x = 35 x = 5 Subt. for x 10 + 3y = 1 3y = -9 y = -3 x + y = 5 + -3 5 - 3 = 2

Total distance covered by Musa in 2 hrs

= x + 10 + 5x

= 6x + 10

Ngozi = 118 km

If they are equal, 6x + 10 = 118

but 6x + 10 < 118

6x < 108

= x < 18

0 < x < 18 = 0 \(\leq\) x < 18