2x(x−2)(x+2)(x2−4)
2xx2−4
xx2−4
4xx2−4
Correct answer is D
1x−2 + 1x+2 + 2xx2−4
= (x+2)+(x−2)+2x(x+2)(x−2)
= 4xx2−4
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=42
x + 3y = 2 .....(ii)
x + 2y = 1.....(i)
x + 3y = 2......(ii)
y = 1
Substitute y = 1 into equation (i)
x+2y=1⟹x+2(1)=1
x+2=1⟹x=−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}