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
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
- Back to worksheet
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