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13.5 Trial and improvement

) Exercise 13.5

1 Find the exact positive solution of each of these equations.
a x² + x = 30 b x² + 4x = 140 c x³ − x = 60 d x(x + 6) = 91

2 Work out a positive solution of each of these equations by trial and improvement.
a x² + x = 3.75 b x² − 2x = 19.25 c x³ + x = 95.625 d x(x + 1)(x + 2) = 1320
3 a Copy this table. x x − 3x
2
Put in the value of x² − 3x when x = 6. 5 10

b Use trial and improvement to find a solution of the equation x² − 3x = 16. 6
Record your trials in the table. Add more rows if you need them.
Give the answer correct to one decimal place.

4 The table shows values of w² − 6w. w w − 6w
2

Use the table to find a solution to each of these equations. 7 7
Give each answer correct to one decimal place. 7.1 7.81
a w² − 6w = 7 b w² − 6w = 9 c w² = 6w + 10
7.2 8.64
7.3 9.49
7.4 10.36

5 Use trial and improvement to find a solution of the equation 2a + a = 30.

2
Start with a = 4. Record your trials in a table.
Give your answer correct to one decimal place.
6 Use trial and improvement to find a positive solution of the equation 5x + x² = 40.

Record your trials in a table.
Give your answer correct to one decimal place.

7 a Read what Jake says. Show that he correct.

x + 10x = 150 has a solution between 8 and 9.
2

b Find the solution to Jake’s equation, correct to one decimal place.
8 Use trial and improvement to find a solution of the equation x²(x + 1) = 6.

Record your trials in a table.
Give your answer correct to one decimal place.
9 Use trial and improvement to find a solution of the equation y³ + y² = 100.

Give your answer correct to one decimal place.
10 The equation 10x − x² = 20 has two solutions.
a One solution is between 2 and 3. Use trial and improvement to find it.

Give the answer correct to one decimal place.
b The other solution is between 7 and 8. Find this, correct to one decimal place.

13 Equations and inequalities 131