## Friday, May 24, 2013

Blog-63

Dear Students,

Following two files are very important to improve your base for remembering the formulas. It is 100 % free for all the students of the world. Download these two files, take the Print Out of these files on two sides of the paper and practice these formulas for your benefit to get high scores in Mathematics Standard 10/ Grade 10.

In the Previous Blog we had seen some important concepts of Quadratic Equation.

Some special and critical types of the factors:
Just go through this downloaded file and be prepared to solve any problem pertaining to these critical factors.

Now we will see important problems of quadratic equations to be solved using perfect square method:

Few steps to be followed to solve the quadratic equation using perfect square method:
1) Shift the constant term to the right hand side of the equation.
2) Divide both sides of the equation by the coefficient of  2.
3) Find the third term of left hand side to make it as a perfect square.
4) Use the formula " Third Term = ( 1/2 coefficient of  x ) 2.
5) Add this third term so obtained as mentioned in step 4 both sides of the equation.

a]  Solve the quadratic equation  x 2 - 18 x  + 65 = 0 using perfect square method.

Solution:
1) Shift 65 to RHS
2)  2 - 18 x  = - 65                  Here third term = ( 1/2 coefficient of  x ) 2
= ( 1/2 (18) 2
= ( 2
= 81
2 - 18 x  + 81 = - 65 + 81
(  - 9 ) 2 = 16
(  - 9 )  = + 4 or  - 9 )  = - 4
= 9 + 4 or   =  9 - 4
= 13 or   =  5
3)  So the roots of the equation are 5 or 13 so Solution Set = { 5, 13 }

b]  Solve the quadratic equation  x 2 - 5 x  + 6 = 0 using perfect square method.

Solution:
1) Shift 6 to RHS
2)  2 - 5 x  = - 6                  Here third term = ( 1/2 coefficient of  x ) 2
= ( 1/2 (5) 2
= ( 5/2 2
= 25/4
2 - 5 x  + 25/4 = - 6 + 25/4
(  - 5/2 ) 2 = (25-24)/4
(  - 5/2 ) 2 = 1/4
(  - 5/2 )  = + 1/2 or  - 5/2 )  = - 1/2
= 5/2 + 1/2 or   =  5/2 - 1/2
= 6/2 or   =  4/2
= 3 or   =  2
3)  So the roots of the equation are 2 or 3 so Solution Set = { 2, 3 }

c]  Solve the quadratic equation  x 2 - 6 x  + 2 = 0 using perfect square method.

Solution:
1) Shift 2 to RHS
2)  2 - 6 x  = - 2                  Here third term = ( 1/2 coefficient of  x ) 2
= ( 1/2 (- 6) 2
= ( - 3 2
= 9
2 - 6 x  + 9 = - 2 + 9
(  - 3 ) 2 =  7
(  - 3 )  = + √ 7 or  - 3 )  = - √ 7
= 3 + √ 7 or   =  3 √ 7
3 + √ 7 or   =  3 - √ 7
3)  So the roots of the equation are 3 + √ 7 or 3 - √ 7 so Solution Set = { 3 + √ 7,  3 - √ 7 }

d]  Solve the quadratic equation  x 2 - 5 x  + 2 = 0 using perfect square method.

Solution:
1) Shift 2 to RHS
2)  2 - 5 x  = - 2                  Here third term = ( 1/2 coefficient of  x ) 2
= ( 1/2 (- 5) 2
= ( - 5/2 2
= 25/4
2 - 5 x  + 25/4 = - 2 + 25/4
(  - 5/2 ) 2 =  (- 8 + 25)/4
(  - 5/2 ) 2 =  17/4
(  - 5/2 )  = + (√ 17)/2 or  - 5/2 )  = -  (√ 17)/2
= 5/2 + (√ 17)/2 or   =  5/2 - (17)/2
= (5 + √ 17)/2 or   =  (5 - √ 17)/2
3)  So the roots are (5 + √ 17)/2 or (5 - √ 17)/2 so Solution Set = { (5 + √ 17)/2,  (5 + √ 17)/2 }

Please write your opinions about the methods given for these problems. My email id is : anil@7pute.com

Few more problems will be discussed in the next Blog.