Q8 - Solve the Following equations (x - 5)(x - 7)(x + 6)(x + 4) - 504 = 0 - Fsc Part 1 Mathematics (Complete Solution) [ Notes, Key book, Solved Exercises, Solved Questions ]

Solutions

As

-5 - 7 + 6 + 4

2

=

-2

2

= -1, So we can write as

[(x - 5)(x + 4)] [(x - 7)(x + 6)] - 504 = 0

(x² + 4x - 5x - 20) (x² + 6x - 7x - 42) - 504 = 0

(x² - x - 20) (x² - x - 42) - 504 = 0

Let x² - x = t and Put in the equation

(t - 20)(t - 42) - 504 = 0

t² - 42t - 20t + 840 - 504 = 0

t² - 62t + 336 = 0

Using the quadratic formula, we have

t =

-(-62) ±

√	(-62)² - 4(1)(336)

2(1)

t =

62 ±

√	3844 - 1344

2

t =

62 ±

√

2500

2

t =

62 ±

√

(50)2

2

t =

62 ±

50

2

Either

t =

62 -

50

2

OR

t =

62 +

50

2

t =

12

2

t =

112

2

t =

6

t =

56

By Letting t = x² - x, Putting the value of t, we get

x² - x = 6

x² - x = 56

x² - x - 6 = 0 --------------(i)

x² - x - 56 = 0 --------------(ii)

By Equation (i) x² - x - 6 = 0

Using the Quadratic formula, we have

x =

-(-1) ±

√	(-1)² - 4(1)(-6)

2(1)

x =

1 ±

√

1 + 24

2

x =

1 ±

√

5

2

x =

1 ±

5

2

Either

x =

1 -

5

2

OR

x =

1 +

5

2

x =

-4

2

x =

6

2

x =

-2

x =

3

By Equation (ii) x² - x - 56 = 0

Using the Quadratic formula, we have

x =

-(-1) ±

√	(-1)² - 4(1)(-56)

2(1)

x =

1 ±

√

1 + 224

2

x =

1 ±

√

225

2

x =

1 ±

√

(15)²

2

x =

1 ±

15

2

Either

x =

1 -

15

2

OR

x =

1 +

15

2

x =

-14

2

x =

16

2

x =

-7

x =

8

Hence the Solution Set of given equation is {-7, -2, 3, 8}

Q8
Solve the Following equations (x - 5)(x - 7)(x + 6)(x + 4) - 504 = 0

Other Topics

Q8 Solve the Following equations (x - 5)(x - 7)(x + 6)(x + 4) - 504 = 0

Other Topics

Q8
Solve the Following equations (x - 5)(x - 7)(x + 6)(x + 4) - 504 = 0