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From Karnataka Open Educational Resources
→Hints for difficult problems
=Hints for difficult problems =
=Hints for difficult problems =
#If P & q are the roots of the equation 2a^-4a+1=0 find the value of
#If P & q are the roots of the equation <math>2a^2-4a+1=0</math> find the value of
p^3+q^3<br>
<math>p^3+q^3</math>
Pre requisites:
'''Pre requisites''':
#Standard form of quadratic equation
#Standard form of quadratic equation
#Formula to find the sum & product of quadratic equation
#Formula to find the sum & product of quadratic equation
#Knowledge of using appropriate identity
#Knowledge of using appropriate identity
Interpretation of the Problem:
'''Interpretation of the Problem''':
#Compare the equation with standard form and identify the values of a,b,c
#Compare the equation with standard form and identify the values of a,b,c
#To find the sum formformof the roots of the quadratic equation using the formula
#To find the sum formformof the roots of the quadratic equation using the formula
#To find the product of the roots of the equation
#To find the product of the roots of the equation
# Using the identity & rewriting p^3+q^3 as (p+q)^3-3pq(p+q)
# Using the identity & rewriting <math>p^3+q^3</math> as <math>(p+q)^3-3pq(p+q)</math>
#Substitute the values of m+n & mn in (p+q)^3-3pq(p+q)
#Substitute the values of m+n & mn in <math>(p+q)^3-3pq(p+q)</math>
#Simplification
#Simplification
Concepts:
'''Concepts''':
#Formula to find the sum and product of the roots of the quadratic equation
#Formula to find the sum and product of the roots of the quadratic equation
#Identity (a+b)^3=a^3+b^3+3ab(a+b)
#Identity <math>(a+b)^3=a^3+b^3+3ab(a+b)</math>
Algorithm: <br>
'''Algorithm''': <br>
Consider the equation 2a^2-4a+1=0<br>
Consider the equation <math>2a^2-4a+1=0</math><br>
Here a=2,b=-4 & c=1<br>
Here a=2,b=-4 & c=1<br>
If p & q are the roots of the quadratic equation then<br>
If p & q are the roots of the quadratic equation then<br>
p+q=-b/a=-(-4)/2=2<br>
<math>p+q={\frac{-b}{a}}={\frac{-(-4)}{2}=2}</math><br>
pq=c/a=1/2<br>
<math>pq={\frac{c}{a}}={\frac{1}{2}}</math><br>
Therefore,<br>
Therefore,<br>
p^3+q^3=(p+q)^3-3pq(p+q)<br> =(2)^3-3(1/2)(2)<br>=
<math>p^3+q^3=(p+q)^3-3pq(p+q)</math><br> =<math>(2)^3-3[{\frac{1}{2}}](2)</math><br>
=8-3<br>=5
3) This process creates a quadratic that is a perfect square, and factoring gives me:<br>
5. Put in the complete square form. (a+b)2 or (a-b) 2<br>
=Ex.no.9.11 /problem no.9=
=Ex.no.9.11 /problem no.9=
