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From Karnataka Open Educational Resources
→Hints for difficult problems
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'''Pre requisites''':
−#Standard form of quadratic equation
−#Formula to find the sum & product of quadratic equation
−#Knowledge of using appropriate identity
−'''Interpretation of the Problem''':
−#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 product of the roots of the equation
−# 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 <math>(p+q)^3-3pq(p+q)</math>
−#Simplification
−'''Concepts''':
−#Formula to find the sum and product of the roots of the quadratic equation
−#Identity <math>(a+b)^3=a^3+b^3+3ab(a+b)</math>
−'''Algorithm''': <br>
−Consider the equation <math>2a^2-4a+1=0</math><br>
−Here a=2,b=-4 & c=1<br>
−If p & q are the roots of the quadratic equation then<br>
−<math>p+q={\frac{-b}{a}}={\frac{-(-4)}{2}=2}</math><br>
−<math>pq={\frac{c}{a}}={\frac{1}{2}}</math><br>
−Therefore,<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
<math>p^3+q^3</math>
<math>p^3+q^3</math>
[[solution]]
[[solution]]
−=Ex.no.9.11 /problem no.9=
=Ex.no.9.11 /problem no.9=
