FACTORING WORKSHEET1 SOLUTION4

In this page factoring worksheet1 solution4 we are going to see solution of some practice questions from factoring worksheet1.

Question 7:

Solve by factoring method [x/(x+1)] + [(x + 1)/x] = 34/15

Solution:

[x/(x+1)] + [(x + 1)/x] = 34/15

[x² + (x + 1) 2]/[x(x + 1)] = 34/15

[x² + (x + 1) 2]/[x² + x] = 34/15

[x² + (x² + 2 x + 1)]/[x² + x] = 34/15

15 (2 x² + 2 x + 1) = 34 (x² + x)

30 x² + 30 x + 15 = 34 x² + 34 x

34 x² - 30 x² + 34 x – 30 x – 15 = 0

4 x² + 4 x – 15 = 0

4 x² + 10 x - 6 x – 15 = 0

2 x (2 x + 5) – 3(2 x + 5) = 0

(2 x – 3) (2 x + 5) = 0

2 x – 3 = 0                    2 x + 5 = 0

  2 x = 3                            2 x = -5

   x = 3/2                             x = -5/2          

Verification:

4 x² + 4 x – 15 = 0

if x = 3/2

4 (3/2)² + 4(3/2) – 15 = 0

9 + 6 - 15 = 0

 15 - 15 = 0

         0 = 0

4 x² + 4 x – 15 = 0

if x = -5/2

4 (-5/2)² + 4 (-5/2) – 15 = 0

(25) - 10 - 15 = 0

25 - 25 = 0

       0 = 0

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Question 8:

a²b²x² – (a² - b²) x + 1 = 0

Solution:

a²b²x² – (a² - b²) x + 1 = 0

a²b²x² – a² x - b² x + 1 = 0

a²x (b² x – 1) -1(b² x – 1) = 0

(b² x – 1) (a² x – 1) = 0

(b² x – 1) = 0                         (a² x – 1) = 0

b² x = 1                                        a² x = 1

     x =1/b²                                      x = 1/a²

Verification:

a²b²x² – (a² - b²) x + 1 = 0

if x = 1/a²

a²b²(1/a²)² – (a² - b²) (1/a²) + 1 = 0

b²/a² - a²/a² + b²/a² + 1 = 0

- 1 + 1 = 0

      0 = 0

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