simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
3
\(\frac{2}{3}\)
7
-4
Correct answer is D
\(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
L.C.M = (3- 2) (3 + 2)
∴ \(\frac{1}{\sqrt{3 - 2}}\) - \(\frac{1}{\sqrt{3 - 2}}\) = \(\frac{\sqrt{3 + 2} - \sqrt{3 - 2}}{\sqrt{3 - 2} + \sqrt{3 - 2}}\)
\(\frac{√3 + 2 - √3 + 2}{3 - 2√3 + 2√3 - 4}\) = \(\frac{4}{3 - 2}\)
= \(\frac{4}{-1}\)
= -4
Solve for y in the equation 10^1 x 5(2y - 2) x 4(y - 1) = 1
\(\frac{3}{4}\)
\(\frac{5}{4}\)
\(\frac{2}{3}\)
5
Correct answer is C
10y x 5(2y - 2) x 4(y - 1) = 1
but 10y - (5 x 2)y = 5y x 2y
= (Law of indices)
5y x 2y x 5(2y - 2) x 4(y - 1) = 1
but 4(y - 1) = 22(y - 1)
= 2y - 2 (Law of indices)
5y x 5(2y -2) x 2(- 2) = 1
5(3y -2) x 2y x 2(2y -2) = 1
= 5(3y -2) x 2(3y -2) = 1
But ao = 1
10(3y -2) = 10o
3y - 2 = 0
∴ y = \(\frac{2}{3}\)
If 9\(^{(x - \frac{1}{2})} = 3^{x2}\) Find x
\(\frac{1}{2}\)
1
2
3
Correct answer is B
9(x - \(\frac{1}{2}\)) 3x2 = 32(x - \(\frac{1}{2}\)) = 3x2
∴ 2(x - \(\frac{1}{2}\)) = x2
2x - 1 = x2
hence x2 - 2x + 1 = 0
(x - 1)(x - 1) = 0
x = 1
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
705
70,000
70,480
70,500
Correct answer is D
\(\frac{3524}{0.05}\) = 70480
\(\approx\) 70500(3 s.g)
1078
1068
718
178
Correct answer is A
\(\begin{array}{c|c} 8 & 71 \\ 8 & 8 \text{rem} 7\\ 8 & 1 \text{rem} 0\end{array}\)
= 1078