3exp fractional equations problem sums involving quadratic equations 1
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Practice
Fractional Equations and Problem Sums involving Quadratic Equations
1. Solve the following equations.
(a)
(b)
(c)
(d)
2. The sides of a right-angled triangle are (x – 3) cm, (x – 1) cm and x cm.
Form an equation involving x and show that it reduces to x2 – 8x + 10 = 0. Hence, find its perimeter.
3. For a journey of 100 km, if the average speed of a vehicle is increased by 5 km/h, the vehicle will arrive 40 minutes earlier. Let the slower average speed be x km/h.
(a) Write down an expression, in terms of x, for the time taken to travel at the slower speed, in hours.
(b) Write down an expression, in terms of x, for the time taken to travel at the increased speed, in hours.
(c) Form an equation in terms of x and show that it reduces to x2 + 5x – 750 = 0.
(d) Solve the equation x2 + 5x – 750 = 0.
(e) Hence, what is the slower average speed? How long, in hours, will the journey take with the increased speed?
4. Find three consecutive integers such that the square of their sum is greater than the sum of their squares by 148.
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x cm
(x – 1) cm
(x – 3) cm
5. Divide 1 into two parts such that the greater part is greater than the sum of the squares of the two parts by 2/25.
6. Solve the equation , giving your answers correct to 2 decimal places.
7. Mr Chan drives 38 km from home to his workplace. He finds that he can save 4 minutes of travelling time if his average speed increases by 4 km/h. Find his original average speed and the corresponding amount of time taken for the journey.
8. A piece of wire of length 80 cm is cut into two parts. One part, 4x cm long, is bent to form a square and the other part is bent into a circle. If the area of the square is equal to the area of the circle, find the value of x, giving your answer correct to 2 decimal places.
9. Solve the equation , y ≠ 0, y ≠ –2.
10. (a) The length of a rectangle is 2x cm and its breadth is 7 cm shorter than its length.Write down an expression, in terms of x, for the area of the rectangle.
(b) Write down an expression, in terms of x, for the area of a square whose length is(x + 4) cm.
(c) Given that the area of the rectangle is equal to the area of the square, form an equation in x, and show that it reduces to 3x2 – 22x – 16 = 0.
(d) Solve the equation 3x2 – 22x – 16 = 0.
(e) Hence, find the difference in perimeters of the rectangle and the square.
End of Practice
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