Evaluate (x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
4x2
(\(\frac{2}{x}\) + 2)2
4
4(1 + x)
Correct answer is D
(x + \(\frac{1}{x}\) + 1)2 - (x + \(\frac{1}{x}\) + 1)2
= (x + \(\frac{1}{x}\) + 1 + x + \(\frac{-1}{x}\) - 1)(x - \(\frac{1}{x}\) + 1 - x + \(\frac{1}{x}\) + 1)
= (2x) (2 + \(\frac{2}{x}\)) = 2x x 2(1 + \(\frac{1}{x}\))
4x (1 + \(\frac{1}{x}\)) = 4x + 4
= 4(1 + x)
Which of the following is a factor of 15 + 7x - 2x2
x + 3
x - 3
x - 5
x + 5
Correct answer is C
Factorize 15 + 7x - 2x2
(5 - x)(3 + 2x); suppose 15 + 7x = 2x2 = 0
∴ (5 - x)(3 + 2x) = 0
x = 5 or x = -\(\frac{3}{2}\)
Since 5 is a root, then (x - 5) is a factor
Make x the subject of the relation \(\frac{1 + ax}{1 - ax}\) = \(\frac{p}{q}\)
\(\frac{p + q}{a(p - q)}\)
\(\frac{p - q}{a(p + q)}\)
\(\frac{p - q}{apq}\)
\(\frac{pq}{a(p - q)}\)
Correct answer is B
\(\frac{1 + ax}{1 - ax}\) = \(\frac{p}{q}\) by cross multiplication,
q(1 + ax) = p(1 - ax)
q + qax = p - pax
qax + pax = p - q
∴ x = \(\frac{p - q}{a(p + q)}\)
If \(\sqrt{x^2 + 9}\) = x + 1, solve for x
5
4
3
2
1
Correct answer is B
\(\sqrt{x^2 + 9}\) = x + 1
x2 + 9 = (x + 1)2 + 1
0 = x2 + 2x + 1 - x2 - 9
= 2x - 8 = 0
2(x - 4) = 0
x = 4
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x
3
4
12
17
Correct answer is A
Principal = N255.00, Interest = 27.00
year = x Rate: 4%
∴ 1 = \(\frac{PRT}{100}\)
27 = \(\frac{225 \times 4 \times T}{100}\)
2700 = 900T
T = 3 years