Factoring Worksheet1 Solution11





In this page factoring worksheet1 solution11 we are going to see solution of some practice questions from factoring worksheet1.

Question 5:

Solve by using quadratic formula a (x² + 1) = x (a² + 1)

Solution:

a (x² + 1) = x (a² + 1)

a x² + a  - x (a² + 1) = 0

a x² - x (a² + 1) + a = 0

Now we are going to compare the given equation by ax² + b x + c = 0

a = a          b = - (a² + 1)          c = a

x = -b ± √(b² – 4 a c)/2a

     = -[- (a² + 1)] ± √([- (a² + 1)]2 – 4 a (a))/2a

     = a² + 1 ± √(a² + 1 + 2a²– 4 a²)/2a

     = a² + 1 ± √(a² + 1 - 2a²)/2a

     = a² + 1 ± √(a² – 1)²/2a

     = a² + 1 ± (a² – 1)/2a

   x = a² + 1 + (a² – 1)/2a            x = a² + 1 - (a² – 1)/2a

   x = (a² + 1 + a² – 1)/2a            x = (a² + 1 - a² + 1)/2a

   x = 2a²/2a            x = 2/2a

   x = a                    x = 1/a

Verification:

a (x² + 1) = x (a² + 1)

if x = 1/a

 a [(1/a)² + 1] = (1/a) (a² + 1)

 a [(1/a²) + 1] = (1/a) (a² + 1)

 a [(1+a²)/] = (a² + 1)/a

(1+a²)/ = (a² + 1)/a

if x = a

 a (x² + 1) = x (a² + 1)

a (a² + 1) = a (a² + 1)


Question 6:

36 x² – 12 a x + (a² - b²) = 0

Solution:

Now we are going to compare the given equation by ax² + b x + c = 0

a = 36    b = - 12 a     c = (a² - b²)

x = -b ± √(b2 – 4 a c)/2a

     = [- (-12 a)] ± √([(-12 a)]² – 4 (36) (a² - b²)/2(36)

     = 12 a ± √144a² – 144 a² + 144 b²/72

     = 12 a ± √144 b²/72

     = (12 a ± 12 b)/72

     = 12 (a ± b)/72

     = (a ± b)/6

x  = (a + b)/6                                x  = (a - b)/6

factoring worksheet1 solution11  factoring worksheet1 solution11