Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
\(\frac{2x}{(x - 2)(x + 2)(x^2 - 4)}\)
\(\frac{2x}{x^2 - 4}\)
\(\frac{x}{x^2 - 4}\)
\(\frac{4x}{x^2 - 4}\)
Correct answer is D
\(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
= \(\frac{(x + 2) + (x - 2) + 2x}{(x + 2)(x - 2)}\)
= \(\frac{4x}{x^2 - 4}\)
If \(5^{(x + 2y)} = 5\) and \(4^{(x + 3y)} = 16\), find \(3^{(x + y)}\).
7
1
3
27
Correct answer is B
\(5^{(x + 2y)} = 5\)
∴ x + 2y = 1.....(i)
\(4^{(x + 3y)} = 16 = 4^2\)
x + 3y = 2 .....(ii)
x + 2y = 1.....(i)
x + 3y = 2......(ii)
y = 1
Substitute y = 1 into equation (i)
\(x + 2y = 1 \implies x + 2(1) = 1\)
\(x + 2 = 1 \implies x = -1\)
\(\therefore 3^{(x + y)} = 3^{(-1 + 1)}\)
\(3^{0} = 1\)
Factorize (4a + 3)2 - (3a - 2)2
(a + 1)(a + 5)
(a - 5)(7a - 1)
(a + 5)(7a + 1)
a(7a + 1)
Correct answer is C
(4a + 3)2 - (3a - 2)2 = a2 - b2
= (a + b)(a - b)
= [(4a + 3) + (3a - 2)][(4a + 3) + (3a - 2)]
= [(4a + 3 + 3a - 2)][(4a + 3 - 3a + 2)]
= (7a + 1)(a + 5)
∴ (a + 5)(7a + 1)
Simplify \(\frac{1}{5x + 5}\) + \(\frac{1}{7x+ 7}\)
\(\frac{12}{35x + 1}\)
\(\frac{1}{35(x + 1)}\)
\(\frac{12x}{35(x + 7)}\)
\(\frac{12}{35x + 35}\)
Correct answer is D
\(\frac{1}{5x + 5}\) + \(\frac{1}{7x+ 7}\) = \(\frac{1}{5(x + 1)}\) + \(\frac{1}{7(x + 1)}\)
= \(\frac{7 + 5}{35(x + 1)}\)
= \(\frac{12}{35(x + 1)}\)
Solve the equation 3x2 + 6x - 2 = 0
x = -1 \(\pm\) \(\frac{\sqrt{3}}{3}\)
x = -1 \(\pm\) \(\frac{\sqrt{15}}{3}\)
x = -2 \(\pm\) 2
x = 3 \(\pm\) \(\frac{\sqrt{3}}{15}\)
Correct answer is B
3x2 + 6x - 2 = 0
Using almighty formula i.e. x = \(\frac{b \pm \sqrt{b^2 - 4ac}}{2a}\)
a = 3, b = 6, c = -2
x = \(\frac{-6 \pm \sqrt{6^2 - 4(3)(-2)}}{2(3)}\)
x = \(\frac{-6 \pm \sqrt{36 + 24}}{6}\)
x = \(\frac{-6 \pm \sqrt{60}}{6}\)
x = \(\frac{-6 \pm \sqrt{4 \times 15}}{6}\)
x = \(-1 \pm \frac{\sqrt{15}}{3}\)