Evaluate$\frac{2}{2 +\sqrt3} + \frac{2 \sqrt3}{2 - \sqrt3} = a + b\sqrt3$

Given that
$\frac{2}{2 +\sqrt3} + \frac{2 \sqrt3}{2 - \sqrt3} = a + b\sqrt3$
where a and b are rational numbers. Find the values of a and b

Answers

$\frac{2}{2 + \sqrt3}$ + $\frac{2\sqrt3}{2 -\sqrt3}$

= $\frac{2(2 -\sqrt3)+ 2\sqrt3 (2 +\; \sqrt3)}{(2 + \sqrt3)(2 \; \sqrt3)}$

= $\frac{4 - 2\sqrt3 + 4\sqrt3 + 2\times 3}{4 - 2\sqrt3 + 2\sqrt3 - 3}$

Combine the Like terms

= $\frac{4\; + 6\; + \; 2\sqrt3}{ 4 - 3}$

= 10 + 2$\sqrt3$ = a + b$\sqrt3$

a = 10 and b = 2

---

johnmulu answered the question on March 7, 2017 at 08:53

Next: Two points P and Q lies on latitude 65^oS. Their longitudes are 96^oE and 84^oW respectively. Find the measured along parallel of latitude. (Take R = 6370 km)
Previous: Find the radius of the circum-circle of a triangle in which angle A = 69^o and a = 3.95 cm.

View More Mathematics Questions and Answers | Return to Questions Index

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

• Two points P and Q lies on latitude 65^oS. Their longitudes are 96^oE and 84^oW respectively. Find the measured along parallel of latitude. (Take R = 6370 km) (Solved)
  

  Two points P and Q lies on latitude 65^oS. Their longitudes are 96^oE and 85^oW respectively. Find the measured along parallel of latitude. (Take R = 6370 km)
  

  Date posted: March 7, 2017.  Answers (1)

• For a given set of data the variance is (2 + x) and the standard deviation is 1.5. Find the value of x(Solved)
  

  For a given set of data the variance is (2 + x) and the standard deviation is 1.5. Find the value of x

  Date posted: March 7, 2017.  Answers (1)

• A man accumulates sh 71 105 after investing sh 50 000 at a rate of 18% p.a. compounded quarterly. Find the time in years taken to accumulate the amount(Solved)
  

  A man accumulates sh 71 105 after investing sh 50 000 at a rate of 18% p.a. compounded quarterly. Find the time in years taken to accumulate the amount

  Date posted: March 7, 2017.  Answers (1)

• The equation of the line L₁ is 5y + 2x + 8 = 0 and L₂ passes through the points (-5,0) and(5, -4). (Solved)
  

  The equation of the line L₁ is 5y + 2x + 8 = 0 and L₂ passes through the points (-5,0) and(5, -4). Without drawing the lines L₁ and L₂, show that the lines are parallel to each other

  Date posted: March 7, 2017.  Answers (1)

• Make x the subject of the formula -n =$\sqrt{\frac{Mx \; - d}{x \; + y}}$(Solved)
  

  Make x the subject of the formula
  -n =$\sqrt{\frac{Mx \; - d}{x \; + y}}$

  Date posted: March 7, 2017.  Answers (1)

• A bus left Nairobi at 8. 00 a.m and travelled towards Kisumu at an average speed of 80 km/hr.(Solved)
  

  A bus left Nairobi at 8. 00 a.m and travelled towards Kisumu at an average speed of 80 km/hr. At 8.30 a.m a car left Kisumu towards Nairobi at an average speed of 120 km/hr. Given that the distance between Nairobi and Kisumu is 400 km, calculate.
  a) The time the car arrived in Nairobi
  b) The time the two vehicles met
  c) The distance from Nairobi to the meeting point
  

  Date posted: March 7, 2017.  Answers (1)

• Determine the amplitude and the period for the graph of (Solved)
  

  Determine the amplitude and the period for the graph of
  6 sin ($\frac{x}{2} - 90^o$)

  Date posted: March 7, 2017.  Answers (1)

• A man deposits his money in a saving bank on monthly basis. Each deposit exceeds the previous by sh 750. If he deposited sh 1500 initially, (Solved)
  

  A man deposits his money in a saving bank on monthly basis. Each deposit exceeds the previous by sh 750. If he deposited sh 1500 initially, how much money will he have deposited in 12 months

  Date posted: March 7, 2017.  Answers (1)

• The equation of a circle 2x² + 8x + 2y² - 10 = 0. Find the radius and the center of the circle(Solved)
  

  The equation of a circle
  2x² + 8x + 2y² - 10 = 0. Find the radius and the centrer of the circle

  Date posted: March 7, 2017.  Answers (1)

• In the expression (x + 2)^x, the sum of the first two terms is 768. Find the value x(Solved)
  

  In the expression (x + 2)^x, the sum of the first two terms is 768. Find the value x

  Date posted: March 7, 2017.  Answers (1)

• A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.(Solved)
  

  A farmer has 1 200 m wire to fence three sides of a rectangular paddock. The fourth side is a wall. Find the dimensions that will give the maximum possible area.

  Date posted: March 7, 2017.  Answers (1)

• A quantity T is partly constant and partly varies as the square root of S. a) Using k and m as the constants, write down an equation connecting T and S(Solved)
  

  A quantity T is partly constant and partly varies as the square root of S.
  a) Using k and m as the constants, write down an equation connecting T and S
  b) If S = 16 when T = 24 and S = 36 when T = 32, find the value of the constants

  Date posted: March 7, 2017.  Answers (1)

• Solve for x in 2(log₂x)² - 7log₂x + log₂8 = 0(Solved)
  

  Solve for x in
  2(log₂x)² - 7log₂x + log₂8 = 0
  Give your answer in surd form

  Date posted: March 7, 2017.  Answers (1)

• $\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form(Solved)
  

  $\frac{\sqrt5 -2\sqrt3}{\sqrt2 + \sqrt{12}}$ is expression in surd form
  i) Write down the conjugate of the denominator in its simplest form
  ii) Hence use the conjugate in (i) above to rationalize the denominator in the expression above

  Date posted: March 7, 2017.  Answers (1)

• The dimensions of a rectangle are given as 8 cm by 5 cm. If A is the area of the rectangle and P is perimeter, determine the maximum possible value of (Solved)
  

  The dimensions of a rectangle are given as 8 cm by 5 cm. If A is the area of the rectangle and P is perimeter, determine the maximum possible value of
  A $\div$ P.

  Date posted: March 7, 2017.  Answers (1)

• A bus P leaves Kisumu at 8 a.m travelling towards Nairobi at an average speed of 70 km/hr.(Solved)
  

  A bus P leaves Kisumu at 8 a.m travelling towards Nairobi at an average speed of 70 km/hr. A matatu Q leaves Kisumu at 9 a.m travelling towards Nairobi at an average speed of 110 km/hr find the distance travelled by Q from Kisumu when it catches up with P.

  Date posted: March 7, 2017.  Answers (1)

• The cost of constructing a road is partly constant and partly varies as the distance. If it costs sh 30 000 to construct a 400 m road and sh 42 000 to construct a road one and half times longer. Find the costs of constructing a 800 m road (Solved)
  

  The cost of constructing a road is partly constant and partly varies as the distance. If it costs sh 30 000 to construct a 400 m road and sh 42 000 to construct a road one and half times longer. Find the costs of constructing a 800 m road

  Date posted: March 7, 2017.  Answers (1)

• The first three terms of geometric progression are the first 4th and progression given that the first term of GP 6.(Solved)
  

  The first three terms of geometric progression are the first 4th and progression given that the first term of GP 6. Find the common difference of the arithmetic progression.

  Date posted: March 6, 2017.  Answers (1)

• A trader mixes two types of sugar, type A and B in the ratio 3:2 to form a mixture which he sells at a price of sh 69.60 per kg in order to make a profit of 20%. (Solved)
  

  A trader mixes two types of sugar, type A and B in the ratio 3:2 to form a mixture which he sells at a price of sh 69.60 per kg in order to make a profit of 20%. If his buying price of type B is sh 70 per kg find the buying price of type A per kg

  Date posted: March 6, 2017.  Answers (1)

• Solve for x in log(x + 5) = log 4 - log(x + 2)(Solved)
  

  Solve for x in
  log(x + 5) = log 4 - log(x + 2)

  Date posted: March 6, 2017.  Answers (1)